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

Question

3. The following questions involve permutations and combinations. You may leave your answer in terms of factorials. (a) (2 points) How many ways can you pick 4 out of 8 people to come to a dinner party? (b) (3 points) There are 10 players on a basketball teamThe first five 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

Hi,
1. since in picking order doesnt matter the total ways are 8C4
2. For the 1st place there can be 5 player choice, for the second 4, for third 3 and so on, total ways 5*4*3*2*1=120
3.Since one position is fixed, that leaves 8 choices, total number of ways is 8! but in this, pitcher can be any spot, so to get the ways where he is 3rd spot, 2 positions are fixed i.e 6! , similarly for 4th spot, 6!
therefore total = 6!+6! = 2*6!
4. we have to choose 3 for Jill and 4 for jack i,e 12C3 * 12C4
Thumbs up if this was helpful, otherwise let me know in comments

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