Question

There are

30

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?

a. There are

nothing

different slates of candidates possible.b. There are

nothing

different ethics subcommittees possible.

Answer 1

(A) chairperson can be seleted in 30 ways

first vice​ chairperson can be seleted in 29 ways

second vice​ chairperson can be seleted in 28 ways

and​ secretary can be seleted in 27 ways

therefore, total number of ways = 30*29*28*27 = 657720 ways

(B) This is a comination case because there is no order in select of members

total number n = 30

and we have to select only 4, so r = 4

using the formula C(n,r) = n!/((n-r)!*r!)

Number of ways = C(30,4)

= 30!/((30-4)!*4!)

= 30!/(26!*4!)

= (30*29*28*27*26!)/(26!*4!)

= (30*29*28*27)/(4*3*2*1)

= 27405