A group of five boys (Alex, Bryan, Chris, David, and Ethan) and six girls (Megan

Question

A group of five boys (Alex, Bryan, Chris, David, and Ethan) and six girls (Megan, Nancy, Olivia, Pauline, Rebecca, and Suzy) are going to sit together in a row of 11 theater seats (a) In how many ways can they seat themselves? (b) In how many ways can they seat themselves if the boys all sit together and the girls all sit together? Submit Answer 18 points My Notes Ask Your Teacher Peg has 6 long-sleeve shirts, 5 short-sleeve shirts, and 5 pairs of pants. (a) How many different ways can Peg dress (assuming she is going to wear a shirt and a pair of pants)? (b) Peg is going on a trip to visit a friend and plans to take 3 shirts and 2 pairs of pants. How many possibilities are there for the articles of clothing she chooses to pack? (c) Peg is going on a trip to the mountains and plans to, again, take 3 shirts and 2 pairs of pants, but since it is supposed to be chilly she decides that the shirts she takes should all be long sleeve. How many possibilities are there for the articles of clothing she chooses to pack? (d) Peg is going on a business trip and plans to, again, take 3 shirts and 2 pairs of pants. This time she decides that of the shirts she takes AT LEAST ONE should be a long sleeve shirt. How many possibilities are there for the articles of clothing she chooses to pack?

Explanation / Answer

Answer to the question is as follows:

Boys:A to E
Girls: M to S

a. They are total 11 in number. So, they can be arranged in (5+6)! = 11! ways = 39916800 ways

b. If boys sit together and girls sit together then ways in which this sitting arragement can happen is:
= Girls arrange between themselves, Boys arrange themselves , then either girls or boys come first:
= 5!*6!*2!
= 172800

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