Help with Discrete Math I Homework #2

[theADOLESCENT]

Hey guys, this is my last homework assignment of the semester and it's on counting. I'm having a little trouble doing it.

 

1) A bridge hand consists of 13 cards from a standard 52 card deck.

How many bridge hands contain cards from exactly two suits?

I said

step 1) pick suits (4 over 2) as in pick 2 suits from 4 suits

step 2)pick cards (26 over 13) as in pick 13 cards from the 26 cards of the two suits you picked in step 1.

 

Answer: (4 over 2)*(26 over 13)

This one I feel pretty good about.

 

2)A club has 25 members: 10 men and 15 women.

In how many ways can a committee of 5 be formed.

Answer: (25 over 5) as in of all 25 people pick 5 for the committee.

This one i feel pretty good about as well

How many of those committees contain at least one woman?

I did (10 over 5) to find out how many committees could be created of all men and then subtracted it from the total number of committees possible.

Answer: (25 over 5)-(10 over 5)

 

3)We have a matrix algebra expression involving the multiplication of 12 matrices.

In how many ways can we completely parenthesize the expression?

 

This one I'm not really sure how to start.

 

4)We have three different children, and 10 different books.

In how many ways can we distribute the books to the children (assume we are allowed to leave children empty-handed).

Answer: 4^10 because you have 10 choices, one for each book; for each book decide if it goes to child #1, 2, 3 or none. This is if we are allowed to keep some of the books for our self and not give some or all away.

 

I'm not sure how to do it for if all of the books have to be given away.

 

Thanks for any help you guys can provide,

theADOLESCENT