Question

A group of 8 workers decides to send a delegation of 3 to their supervisor to discuss their grievances. Complete parts​ (a) through​ (c) below. ​(a) How many delegations are​ possible? There are 33656 56 delegations possible. ​(b) If it is decided that a particular worker must be in the​ delegation, how many different delegations are​ possible? There are 100.8 1008 delegations possible.

Answer 1

A) 56

B) 21

Explanation:

A) The number of delegations possible is given by;

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

In this question, n = 8 and r =3

Thus,

C(8,3) = 8!/[(8 - 3)!(3!)] = 56

B) Since a particular member must be in the delegation, the number of outcomes will now be;

C(n, r) - C(n-1,r)

Thus, we have;

C(8,3) - C(7,3)

= 56 - [7!/[(7 - 3)!(3!)]

= 56 - 35 = 21