₦airaland Forum

Yankee101:
Give a person money and freedom and see their true colors

God knows alot of people will become terrible people if they ever grow rich

Go figure

Exactly. Some become snubbish, arrogant and nasty when they have money. You will see them on the road and they will snub you when you try to say "hi". I remember one uncle that started giving everyone attitude because he was rich. He was very arrogant. He would talk to people anyhow, snub close friends and treat them like trash, etc. Defeat him in an argument or tell him what he doesn't like hear and he start insulting you for being broke (that's if you are broke). He became humble when things became hard and he went broke . Each time I see him, I try to contain my laughter. This experience made me ask if many poor people that are humble are just humble because they have nothing.

4) To show that C(n, r) = C(n, n - r)

FROM LHS :
C(n, r) = (n!) / [(r!)(n - r)!]
r! = [ n - (n - r) ]!
(n!)/ [(r!)(n - r)!] = (n!) / ( [n - (n - r)]!(n - r)! )
if d = (n - r)
(n!) / ( [n - (n - r)]! (n - r)! ) = (n!) / [(n - d)!(d!)]
= C(n, d) = C(n, n - r)

FROM RHS :
C(n, n - r) = (n!) / [ (n - r)! [n - (n - r)]! ]
n - (n - r) = r
(n!) / [ (n - r)! [n - (n - r)]! ] = (n!) / [(r!)(n - r)!]
= C(n, r)

∴ C(n, r) = C(n, n - r)

5) To show C(n, r) + C(n, n - r) = C(n+1, r)

I've shown in the previous proof that C(n, r) = C(n, n - r) . Hence

C(n, r) + C(n, n - r) = 2 C(n, r) = 2 C(n, n - r) = C(n+1, r)
∴ on simplification,
C(n+1, r) = 2 C(n, r) = [(2)(n!)] / [(r!)(n - r)!]

We begin with C(n+1, r) . Observe that

C(n+1, r) = (n + 1)! / [ (r!)(n + 1 - r)! ]
= [ (n + 1)(n!) ] / [ (r!)(n + 1 - r)(n - r)! ]
= [ (n + 1)/(n + 1 - r) ] × [ (n!) / [(r!)(n - r)!] ]
= [ (n + 1)/(n + 1 - r) ] C(n, r)

Since [ (n + 1)/(n + 1 - r) ] ≠ 2 for any arbitrary choices of n and r , we can say that the statement C(n, r) + C(n, n - r) = C(n+1, r) is invalid except for n and r choices that simultaneously satisfy the linear equation n - 2r + 1 = 0

Sl2348, I have completed your assignment.

Lol. This is very simple na. Check out the maths challenges I gave and see if you can solve it. If no mathematician on nairaland can solve it, I will post the solution in 3 days time. Try your luck.

Before solving here are things to note:
1) P(n, r) = (n!)/(n - r)! , 2) C(n, r) = (n!)/ [ r!(n - r)! ]
3) 0! = 1! = 1 and
4) n! = n(n - 1)(n - 2)(n - 3)... × 3 × 2 × 1, n is an integer & n ≥ 2.

With these, let's get on with it.

1) To show (n + 1) P(n, n) = P(n+1, n)

FROM LHS :
(n + 1) P(n, n) = (n + 1) [(n!)/(n - n)!]
= [(n + 1)(n!)] / (n - n)! = (n + 1)! / (n - n)!
since (n - n)! = 0! = 1 = 1! , you have (n - n)! = 1! = [(n + 1) - n]!
[(n + 1)!/(n - n)! ] = [ (n + 1)! / [(n+1) - n]! ]
= P(n+1, n)

FROM RHS :
P(n+1, n) = (n + 1)! / [(n+1) - n]!
since [(n+1) - n]! = 1! = 0! = (n - n)! ,
= ( [(n + 1)(n!)] / [(n+1) - n]! )
= (n + 1) [(n!)/(n - n)!] = (n + 1) P(n, n)

∴ (n + 1) P(n, n) = P(n+1, n)

2) to show that P(n, r+1) = (n - r) P(n, r)

FROM LHS :
P(n, r+1) = (n!) / [n - (r+1)]!
multiplying and dividing by (n - r)!
= [(n - r)(n!)] / [ (n - r)[n - (r+1)]! ]
= [(n - r)(n!)] / (n - r)! = (n - r)[(n!)/(n - r)!]
= (n - r) P(n, r)

FROM RHS : simply use the above workings to work backwards to show (n - r) P(n, r) can be rewritten as P(n, r+1)

3) To show that P(n, r) = (r!) C(n, r)

FROM LHS :
P(n, r) = (n!)/(n - r)!
multiplying and dividing by r! ,
P(n, r) = [(r!)(n!)] / [(r!)(n - r)!]
= (r!) [ (n!)/ [(r!)(n - r)!] ] = r! C(n, r)

FROM RHS :
C(n, r) = (n!) / [(r!)(n - r)!]
r! C(n, r) = [(r!)(n!)] / [(r!)(n - r)!] = (n!)/(n - r)!
r! C(n, r) = P(n, r)

∴ P(n, r) = r! C(n, r)

Can't remember all my scores as an undergraduate. I just look at my grade. Never been a top scorer but my highests have been 80 - 88.

stanech:
TDS is real

.
@UMich
student Halley Bass told police a Trump supporter attacked her by scratching her face in Nov 2016. She said she was targeted for wearing a pin in support of UK Remain. As her story fell apart, she admitted to scratching herself.

In autumn 2018 at @KState U, a note was left on an apartment that read "Beware n***ers live here! Knock at your own risk." The "victim" admitted to police that s/he did it himself. This was the 2nd time s/he had fabricated a hate incident in 2 years.

In Nov 2017 near @KState University, a black man's car was vandalized with racist messages. Class was cancelled & students held demonstrations. Dauntarius Williams later admitted to police that he did it himself. Police did not charge him.




In Nov 2016 a black female student at @VillanovaU in PA said a group of white men yelling "Trump!" knocked her to the ground on campus. However a police & university investigation was halted because the student didn't want to pursue the matter.

In Nov 2016 a Philadelphia neighborhood was rattled when property was vandalized with pro-Trump and anti-black messages. William Tucker a democrat was identified as the vandal through CCTV footage


@StOlaf College was roiled by mass protests in response to anti-black notes found across campus. Class was cancelled & admin caved to demands. An investigation found that Samantha Wells, a black victim of one of the notes, fabricated the incident.



In Nov 2018 students at Goucher College demanded social justice training & safe spaces after racist, Nazi, & KKK graffiti was found on campus. Someone even wrote the names of black students. Trump was blamed.

Fynn Arthur, a black student, was responsible

In Sep. 2018 a black woman in Long Island said Trump supporters confronted her & told her “she didn’t belong here.” Her car tire was slashed the next day & a hateful note was left behind saying “go home.”
Adwoa Lewis made up the whole story.


In Dec 2016 a Muslim woman said she was attacked by 3 white Trump supporters in NYC on the subway. She said they tried to rip off her hijab.
Yasmin Seweid lied. CAIR said Muslims are under tremendous “stress & pressure” resulting in incidents like this.


I remember that Trump & his supporters were blamed for a spate of anti-Semitic, KKK & Nazi graffiti on the campus of Nassau Community College in Long Island in late 2016. The student responsible was Jasskirat Saini: not white


In Nov 2016 a Muslim student at the University of Louisiana said two white racist Trump supporters brutally assaulted her, ripped off her hijab, & robbed her. The story went viral.
It was a lie. Media never identified her by name after hoax was revealed.


One week before the presidential election, a black church in Mississippi was burned in an arson attack. “Vote Trump” was written on the building. After much panic, an investigation revealed that the man responsible was a church member. Andrew McClinton:


Days after the Pittsburgh massacre, Trump supporters were blamed for Nazi vandalism at a Brooklyn synagogue & fires in a Jewish community. Turns out the perpetrator was a gay black man who had worked with city council on an initiative to fight hate crimes

When they can't find any evidence that Trump and his supporters are full of hate, they invent one.

stanech:
Really? You think this is fake news? Wake up my friend


The biggest problem in Sweden is that their government is trying so hard to hide these crimes.

When CNN brands your source as fake news and Russian propaganda (Lol ), know that your source is reliable.

stanech:
Achievements of the worlds first "feminist" government in Sweden

- 40 000 women genitally mutilated in Sweden
- 7 840 reported rapes last year (new record)
- Half of reported rapes are against children
- 50% of women afraid to go outside alone in some areas

What went wrong?�

Lol. You are Islamophobic for posting these facts.

Don't you know people are good and moral relativism is true. Even though men from core Islamic countries don't respect and hate white women and western culture, it's still okay to let them in without any background checks and mix with people. Your shall not criticise their religion, point out their Islamic motivated crimes against the western people and culture or point out their intentions of Islamisation. Stanech, stop being islamophobic. You are a racist, xenophobic, homophobic, misogynistic and sexist piece of sh1t.

Lol. No one is forcing you to take the job.

LiveByNight:
Nigerians have forgotten what it means to live like a human being. They assume their current state of existence is actually normal without realizing that 98% of them live in a sub human state, all because of fear.

They have forgotten it is better to die on your feet than to live on your knees. Nigerians are born into servitude to the elite and hence will continue to live on their knees forever

People would rather kill the innocent for little bread than stand up to their oppressors and fight for a better life.

Freedom of expression makes a faceless forum interesting and colourful. Seun knows that.

Before you know am, she don become billionaire.

I thought I saw this picture in a documentary where they were talking about evolution and our primitive ancestors.

Tallesty1:
In 1970,the population of Nigeria was 55 million same as Britain.



Today's Nigeria is over 200 million and Britain's is just 64 million, this includes immigrants from across the world.

Your country still don't have a stable electricity and what you think is the solution to our problem is marrying many wives to have more sex.


Do you see how unreasonable you sound? Muslim men cheat very well, they just do it codedly and their women are used to it that is why you don't hear about it because they don't complain so get your facts right before you take a swipe on Christians

Don't mind him. The country is hard but you see Nigerians giving birth to children that they can't take care of. Whether we like it or not, giving birth to children you can't take care of is one of the core causes of suffering, crime and poverty in this world.

MJBOLT:

big disrespect to atletico fans,UEFA should not hesistate to sanction the arrogant pr*ck

Atletico fans were booing him. Big disrespect to Ronaldo, UEFA should not hesitate to sanction the disrespectful and ill mannered crowd.

HazzanTazzan:
U just don’t get it... do you?

What prompted the gesture made by Ronaldo?

He didn’t do that cos he lost the game... he did it cos he was booed...

It was a very perfect response

Are you minding Nbote? Ronaldo haters must hate no matter what even if it means sacrificing reasoning.

The attention seeker got what he deserves. If it were to be woman found falsely accusing someone of rape, nothing would happen even if her victim has spent years in jail.

femidejulius:
Despite the prevalent use of juju, why don't African teams win the world cup? Why don't the players win the best fifa player award?

Abi o.

If the lady in brown is not employed, call me a bast@rd. Congrats Ma, you've secured the bag.

satowind:
2 benzimeter

I saw her in a Nigerian Benz factory. I asked what she was doing there and I was told that she was their raw material for manufacturing Benz na so I ja commot before I turn raw material.

infogenius:
When God answers ur call. Never forget to relate with Him the way u did b4 He answered ur call.
This family I guess put God one side when fame came.

Oh my goodness. What the heck is this?

dlw09:
Muslims are more secular in China, and can coexist peacefully with other religions.
Can you take a look at the picture below, Chinese Muslims, different from what you imagined?

Great.

asiwaju:
i think Baba Suwe also need counselling because he is also suffering from Poverty and Depression.i listened to him on Kola Olootu Radio Show and you can see from the way he was talking that,not only was he sick,he is also suffering from Poverty and depression.(He said,he need 100Million Naira to take care of himself and that 5Million Naira is not Money,Only People who has seen real Money will call 5Million Naira in the present day Nigeria a small money,He also said Asiwaju Tinubu gave him 1Million Naira of recent and that Tinubu is his junior Brother)He need serious Counselling and psychotherapeutic treatment,May God Heal Him Amen.

Lol. He needs to adjust to his situation and start cutting his coat according to his size. He sounds arrogant and entitled because he was very rich before.

How do you know that bullet refused to enter his body?

A barber in my street is owing me #500. Oga has been avoiding me.

dlw09:
haha,

If you have the chance, you can come to China to see if it is real

There is a mosque near my house

Do Muslims in China give you guys trouble? For example do they get violent when you exhibit your freedom of speech by insulting their sacred beliefs, drawing prophet Muhammad ? Do they try to push their beliefs and sharia into the constitution and people? Do they rape and treat their women badly? Do they hold any hostility towards non-Muslims?

I concur.

So he did not reciprocate Juliet Ibrahim's green light?

They are among the most beautiful women in the world.

She behaved exactly like the GNLD guy that approached me.