3. The following questions involve permutations and combinations. You may lkeave

Question

3. The following questions involve permutations and combinations. You may lkeave your answer in factorials. answer in terms of (a) (2 points) How many ways can you pick 4 out of s people to come to a dinner party? (b) (3 points) There are 10 players on a basketban team The first fire starting players are introduced one at a time. In how many different ways can they be introduced (c) (5 points) How many batting orders are possible for a team of nine baseball players in which the pitcher always bats last and the first baseman bats in either the third or fourth spot? (d) (5 points) Fred has 12 books. He plans to give three books to Jill and four books to Jack. How many different ways are there for him to do this?

Explanation / Answer

Solution:

( a )

number of ways of picking 4 out of 8 people for a dinner party = 8c4 = 70

( b )

number of ways of placing 5 out of 10 players for introcuction one at a time = 10p5 = 30240

( c )

number of batting orders possible in which the pitcher bats last and first baseman bats at either 3rd or 4th spot

= 1 * 1 * 7! + 1 * 1 * 7!

= 5040 + 5040

= 10080

( d )

number of ways to give 3 books to jill and 4 books to jack = 12c3 * 9c4 = 220 * 126 = 27720

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