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**Jhua4****Member**- Registered: 2012-12-03
- Posts: 12

1) suppose you have 70 books (35 novels, 20 history books and 15 math books). Assume that all 70 books are different

A) in how many different ways can you put 70 books in a row on a shelf?

B) in how many different ways can you choose a set of 12 books to give to a friend?

C) in how many different ways can you choose a set of 4 history books and 8 novels to give to a friend?

D) in how many different ways can you put the 70 books in a row on a shelf if the novels are on the left, the math books are in the middle and the history books are on the right?

2) what is the coefficient of x^40 and y^10 in the expansion of (2x+y)^50?

3) give a simple expression for the value of the following sum (as a function of n):

C(n,0) + 3 * C(n,1) + 3^2 * C(n,2) +...+ 3^n-1 * C(n,n-1) + 3^n * C(n,n).

Your formula should not involve sums or combinatorial symbols like P(n,r) or C(n,r). Using the binomial theorem briefly justify why your answer is correct.

4) you have 20 pennies, 60 nickels and 40 dimes. Assume that the pennies, dimes and nickels are identical. In how many different ways can you put all the coins in a row?

5) assume we are using LaPlace's probability model, where all outcomes are equally likely. An urn contains 70 balls, of which 10 are red, 20 are blue and 40 are green. Let b be a randomly chosen ball.

A) what is p(b is not green)?

B) what is p(b is blue | b is not red)?

Please help with these questions! Thanks!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,249

Hi Jhua4;

That looks like an entire course worth of work.

I have answered 3 very tough problems in the other thread. I did that because you are new and I want to help.

I do not do homework problems or test problems unless you show some work, some effort.

I am willing to go over the problems one at a time.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**Jhua4****Member**- Registered: 2012-12-03
- Posts: 12

I worked through them all but am not sure if they're correct.

For question

1a) I have 70!

B) C(70,12)

C) C(35,8)*C(20,4)*C(15,0)

D) 35!*20!*15!

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**Jhua4****Member**- Registered: 2012-12-03
- Posts: 12

2) 2^40 (50,10)

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,249

Hi;

A and B are correct.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**Jhua4****Member**- Registered: 2012-12-03
- Posts: 12

3) 4^n

4) 120!/20!60!40!

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**Jhua4****Member**- Registered: 2012-12-03
- Posts: 12

5a) 3/7

B) 1/3

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,249

Hi;

2) I get

which is confirmed by direct computation.

4) Is correct. Just a standard Mississippi problem.

5) Please state what you mean by the LaPlace's probability model.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**PeterG****Guest**

Jhua4 wrote:

3) 4^n

4) 120!/20!60!40!

How do you solve #3??? I cannot find that anywhere... I am sure it is simple, but I cant get it!

I had this problem:

Give a simple expression for the value of the following sum (as a function of n).

that is supposed to be +...+6^(n-1) -- looks like the math script is a bit broken

This is not homework -- it is a problem on a previous test.. I can't figure it out.

I am guessing Jhua4 is from UCI as well, Dillenc0urt?

THANK YOU!:D

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

hi PeterG

Welcome to the forum.

Follow ^ with {} brackets to get the layout you want:

The question needs the binomial formula:

http://www.mathsisfun.com/algebra/binomial-theorem.html

Using that formula try putting a = 1, b = 6

Notation:

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**PeterG****Guest**

bob bundy wrote:

hi PeterG

Welcome to the forum.

Follow ^ with {} brackets to get the layout you want:

The question needs the binomial formula:

Using that formula try putting a = 1, b = 6

Notation:

Bob

so how does it get to

I must be missing a step:

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Hi PeterG

Do you know how the binomial formula goes?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**PeterG****Guest**

anonimnystefy wrote:

Hi PeterG

Do you know how the binomial formula goes?

Yes,

I am sorry, but I am tired -- finals are friday, lots of subjects -- I can solve binomial for other cases, not this one, I am just brain farting and no one is helping...

If I didn't need help I wouldn't ask!

**PeterG****Guest**

PeterG wrote:

anonimnystefy wrote:Hi PeterG

Do you know how the binomial formula goes?

Yes,

I am sorry, but I am tired -- finals are friday, lots of subjects -- I can solve binomial for other cases, not this one, I am just brain farting and no one is helping...

If I didn't need help I wouldn't ask!

Wth...

You know this is a trick question, expanding and what not... wth -- like a couple hours on that complete nonsense!!!

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

OK. Like this:

No 'a's appear in the question you had so put a = 1 and all the a powers are just 1.

Put b = 6.

And that's it because the LHS is 7^n and the RHS is what you were asked to simplify.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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