SOLUTION: Assume a class has 24 members. (a) In how many ways can a president, a vice president, and a secretary be selected? The formula is nPr= n!/(n-r)!

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Question 1161761: Assume a class has 24 members. (a) In how many ways can a president, a vice president, and a secretary be selected? The formula is nPr= n!/(n-r)!
(b) How many committees of 5 people can be chosen? The formula is
nCr= n!/r!(n-r)!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Assume a class has 24 members.

(a) In how many ways can a president, a vice+president, and a secretary+be selected?

The formula is

nPr=+n%21%2F%28n-r%29%21+....given n=24 and r=3

24P3=+24%21%2F%2824-3%29%21+

24P3=+24%21%2F21%21+

24P3=+%28%2824%2A23%2A22%29%2A21%21%29%2F21%21+

24P3=+%28%2824%2A23%2A22%29%2Across%2821%21%29%29%2Fcross%2821%21%29+

24P3=+24%2A23%2A22+

24P3=+12144+


(b) How many committees of 5 people can be chosen?

The formula is:


24C5=+24%21%2F%285%21%2824-5%29%21%29.....given n=24 and r=5

24C5=+24%21%2F%285%21%2A19%21%29

24C5=+%28%2824%2A23%2A22%2A21%2A20%29%2A19%21%29%2F%285%21%2A19%21%29......simplify

24C5=+%28%2824%2A23%2A22%2A21%2A20%29%2Across%2819%21%29%29%2F%285%21%2Across%2819%21%29%29

24C5=+%2824%2A23%2A22%2A21%2A20%29%2F%285%21%29

24C5=+%2824%2A23%2A22%2A21%2A20%29%2F%285%2A4%2A3%2A2%2A1%29



24C5=+24%2A23%2A11%2A7

24C5=+42504