Question

In how many different ways can a ski club consisting of 20 people select a person for its officers? The positions available are president, vice president, treasurer, and secretary. No person can hold more than one positions and the each office is filled in order.
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A)74


B) 116,280


C) 1440


D) 4845

Answer 1

Answer:

4845

Step-by-step explanation:

$\frac{20*19*18*17}{4*3*2*1} = 4845$

Answer 2

Answer:

D. 4845ways

Step-by-step explanation:

Combination has to do with selection.

To select r object from pool of n objects, this can be expressed using the combination formula

nCr = n!/(n-r)!r!

According to the question, total number of people in the ski club is 20 i.e n=20

If the positions available are president, vice president, treasurer, and secretary, this shows that we need to select 4people to from the pool of 20 to fill the positions. This can be done in 20C4 number of ways.

20C4 = 20!/(20-4)!4!

20C4 = 20!/16!4!

20C4 = 20×19×18×17×16!/16!×4×3×2×1

20C4 = 20×19×18×17/24

20C4 = 4845

This can be done in 4845ways