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(a) A certain committee consists of 16 people. From the committee, a president, a vice-president, a secretary, and a treasurer are to be chosen. In how many ways can these 4 offices be filled? Assume that a committee member can hold at most one of these offices.

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(b) A company has 37 salespeople. A board member at the company asks for a list of the top 5 salespeople, ranked in order of effectiveness. How many such rankings are possible?

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(a) A certain committee consists of $16$ people. From the committee, a president, a vice-president, a secretary, and a treasurer are to be chosen. In how many ways can these $4$ offices be filled? Assume that a committee member can hold at most one of these offices. $\newline$ $\square$ $\newline$ (b) A company has $37$ salespeople. A board member at the company asks for a list of the top $5$ salespeople, ranked in order of effectiveness. How many such rankings are possible? $\newline$ $\square$

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Experimental probability

Full solution

Q. (a) A certain committee consists of

16

people. From the committee, a president, a vice-president, a secretary, and a treasurer are to be chosen. In how many ways can these

4

offices be filled? Assume that a committee member can hold at most one of these offices.

\newline

\square

\newline

(b) A company has

37

salespeople. A board member at the company asks for a list of the top

5

salespeople, ranked in order of effectiveness. How many such rankings are possible?

\newline

\square

Calculate Offices Selection: Calculate the number of ways to choose a president, vice-president, secretary, and treasurer from $16$ people, where each person can hold only one office. Use the permutation formula since the order in which the offices are filled matters. $\newline$ Calculation: $16 \times 15 \times 14 \times 13 = 43,680$
Rank Top Salespeople: Calculate the number of ways to rank the top $5$ salespeople from a group of $37$ . Use the permutation formula because the order of ranking is important. $\newline$ Calculation: $37 \times 36 \times 35 \times 34 \times 33 = 45,297,120$

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