There are 18 people to choose from for a six-person volleyball team. Four of the
ID: 3360865 • Letter: T
Question
There are 18 people to choose from for a six-person volleyball team. Four of the 18 people are women, and the other 14 are men. a) How many ways can a six-person volleyball team can be selected from any of the 18 people? b) How many different ways can a six-person volleyball team can be selected if the team must have exactly 1 woman AND 5 men, OR 2 women AND 4 men? Hint: Decide how many ways can the women be selected AND then how many ways for the men. c) What is the probability that a random selection produces a team with no women?Explanation / Answer
a) Six person team can be selected from 18 people in
18C6 = 18564 ways.
b) If we select 1 woman and 5 men, we can select the team in
4C1 * 14C5 = 4 * 2002 = 8008 ways.
If we select 2 women and 4 men, we can select the team in
4C2 * 14C4 = 6 * 1001 = 6006 ways.
=> The number of ways to select 1 woman and 5 men or 2 women and 4 men
= 8008 + 6006 = 14014.
c) The number of ways we can select a six-person team with no women = 14C6
=> Probability of selecting a team with no women = 14C6 / 18C6
= 3003 / 18564
= 0.1618.
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