Question

There are 58 members on the board of directors for a certain non-profit institution.a.If they must elect a chairperson, first vice chairperson, second vice-chairperson, and secretary, how many different slates of candidates are possible?b.If they must form an ethics subcommittee of four members, how many different subcommittees are possible?

Answer 1

a. 10182480

b. 424270

Step-by-step explanation:

a. There are 58 members on the board of directors, i.e n = 58.

The number of elected candidates, r = 4

⇒ The number of different slates of candidates possible can be calculated by

P(n, r) = n!/(n-r)!

P(58, 4) = 58!/(58 -4)!

P(58, 4) = 58!/54!

P(58, 4) = 58 x 57 x 56 x 55 x 54!/54!

P(58, 4) = 58 x 57 x 56 x 55

P(58, 4) = 10182480

⇒ 10182480 different slates of candidates are possible

b. The number of possible different subcommittees is given by

C(n, r) = n!/r!(n-r)!

C(n, r) = 58!/4! (58 - 4)!

C(n, r) = 58!/4! x 54!

C(n, r) = 58 x 57 x 56 x 55 x 54!!/54! x 4 x 3 x 2 x 1

C(n, r) = 58 x 57 x 56 x 55 / 4 x 3 x 2 x 1

C(n, r) = 10182480/24

C(n, r) = 424270

∴ 424270 possible different subcommittees can be formed.