Answer the questions below.(If necessary, consult a list of formulas.)(a) A certain committee consists of 18 people. From the committee, a president, a vice-president, and a treasurer are to be chosen. In how many ways can these 3 offices be filled? Assume that a committee member can hold at most one of these offices.(b) From a collection of 52 store customers, 2 are to be chosen to receive a special gift. How many groups of 2 customers are possible?
Question
Answer the questions below.(If necessary, consult a list of formulas.)(a) A certain committee consists of 18 people. From the committee, a president, a vice-president, and a treasurer are to be chosen. In how many ways can these 3 offices be filled? Assume that a committee member can hold at most one of these offices.(b) From a collection of 52 store customers, 2 are to be chosen to receive a special gift. How many groups of 2 customers are possible?
Solution
(a) The number of ways to fill these 3 offices can be calculated using the formula for permutations of a set, which is nPr = n! / (n-r)!. Here, n is the total number of items to choose from, and r is the number of items to choose.
For the president, we have 18 choices. For the vice-president, we have 17 choices left (since one person has already been chosen as president). For the treasurer, we have 16 choices left. So, the total number of ways to fill these 3 offices is 181716 = 4896 ways.
(b) The number of ways to choose 2 customers from 52 can be calculated using the formula for combinations of a set, which is nCr = n! / [r!(n-r)!]. Here, n is the total number of items to choose from, and r is the number of items to choose.
So, the number of ways to choose 2 customers from 52 is 52C2 = 52! / [2!(52-2)!] = 1326 ways.
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