Question

From a group of 8 volunteers, including Andrew and Karen, 4 people are to be selected at random to organize a charity event. What is the probability that Andrew will be among the 4 volunteers selected and Karen will not?
A. 3/7
B. 5/12
C. 27/70
D. 2/7
E. 9/35

Answer 1

Answer:

The correct option is D. 2/7

Step-by-step explanation:

Consider the provided information.

There are 8 volunteers including Andrew and Karen, 4 people are to be selected at random to organize a charity event.

We need to determine the probability Andrew will be among the 4 volunteers selected and Karen will not.

We want to select Andrew and 3 others but not Karen in the group.

Thus, the number of ways to select 3 member out of 8-2=6

(We subtract 2 from 8 because Andrew is already selected and we don't want Karen to be selected, so subtract 2 from 8.)

The required probability is:

$\dfrac{^6C_3}{^8C_4}=\dfrac{\frac{6!}{3!3!}}{\frac{8!}{4!4!}}\\\\\\\dfrac{^6C_3}{^8C_4}=\frac{20}{70}\\\\\\\dfrac{^6C_3}{^8C_4}=\dfrac{2}{7}$

Hence, the correct option is D. 2/7