Question

1. A six person committee composed of Alice, Ben, Connie, Dolph, Egbert, and Francisco is to select a chairperson, secretary, and treasurer. How many different officer selections are there if both Dolph and Francisco must hold office?

Answer 1

Answer:

The number of combinations are made when one person taken at a time out of four person=4.

Step-by-step explanation:

We are given that a six person committee composed of Alice,Ben,Connie, Dolph,Egbert, and Francisco.

We have to select three persons out of six persons one is chairperson,secretary and treasurer.

We have to find the number of combinations of different officer are made when two persons Dolph and Francisco must hold office.

Now, if two persons Dolph and Francisco must hold the office then we have to select only one member out of 4 persons.

Therefore ,using combination formula

$\binom{n}{r}$=$\frac{n!}{r!(n-r)!}$

We have n=4 and r=1 then

The number of combination of different officer are made =$\binom{4}{1}$

The number of combination of different officer are made=$\frac{4!}{1!(4-1)!}$

The number of combination of different officer are made=$\frac{4\times 3!}{3!}$

The number of combination of different officer are made=4

Hence, the number of combinations are made when one person taken at a time out of four person=4.

Answer: 4