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A group of three women and seven men have been nominated for a 3-person committee. One
Chapter 8, Problem 6(choose chapter or problem)
A group of three women and seven men have been nominated for a 3-person committee. One person serves a 1-year term, one a 2-year term and the third a 3-year term. In how many ways can three people be chosen for this committee if (a) every person is eligible? (b) only the men are eligible? (c) at least one woman must be selected? (d) at least one woman and at least one man are to be selected?
Questions & Answers
QUESTION:
A group of three women and seven men have been nominated for a 3-person committee. One person serves a 1-year term, one a 2-year term and the third a 3-year term. In how many ways can three people be chosen for this committee if (a) every person is eligible? (b) only the men are eligible? (c) at least one woman must be selected? (d) at least one woman and at least one man are to be selected?
ANSWER:Step 1 of 5
Permutation and combination formulas are helpful to find the permutation and combination of r objects taken from n objects. The concept of permutations is used to find the different arrangements and the concept of combinations is used to find the different groups. For the given values of n and r, the permutations are always greater than the combinations.
Formulas:
Factorial:
Combination:
Permutation:
