Answer:
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.