only question 6,7 and 8!

typed answers required.

MATH 464

HOMEWORK 6

SPRING 2013

The following assignment is to be turned in on

Thursday, March 7, 2013.

1. Suppose that in a certain state the license plates have three letters fol-

lowed by 3 numbers. If no letter or number can be repeated, how many

license plates are possible?

2. A club has 50 members. The club need to form two committees, one with

8 members and one with 7 members. How many ways can this be done if

no one is allowed to serve on two committees at the same time?

3. 6 students, 3 boys and 3 girls, line up in random order for a photograph.

What is the probability that the boys and girls alternate?

4. A fair coin is tossed 10 times. What is the probability of 5 heads? What

is the probability of at least 5 heads?

5. I have a television with 50 channels. On a certain evening, 12 are showing

sit-coms, 17 are showing reality shows, 15 are showing movies, and the

remaining 6 are showing something else. If I randomly pick 5 of the channels

and look at what is showing, what is the probability that I see:

a) exactly 2 movies, 1 sit-com, and 2 reality shows?

b) at least one movie?

c) only sit-coms and reality shows?

6. Consider a usual deck of cards. Draw five cards at random. What is the

probability you get:

a) ”four of a kind” or four cards of the same rank?

b) a ”full-house” or three cards of the same rank and two cards of the same

rank?

c) ”three of a kind” or three cards of the same rank, but you do not have a

”full-house”?

7. I have 4 friends and 15 cookies. How many ways are there to:

1

2 SPRING 2013

a) give away all the cookies with no constraints?

b) give away all the cookies making sure every friend gets at least 2 cookies?

c) give away some (or none) of the cookies with no constraints?

8. A round table has n seats. n people are seated at random around the

table. Fred, who is sitting at the table, dislikes two of the people. Let X be

the number of neighbors of Fred whom he dislikes. Find the p.m.f. of X.

(Note that X can only be 0, 1, 2. )

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