From a Group of 8 People, Including George and Nina, 3 people are to be selected at random to work on a certain project.

BTGmoderatorDC wrote: ↑

Fri Apr 07, 2023 3:49 am

From a Group of 8 People, Including George and Nina, 3 people are to be selected at random to work on a certain project. What is the probability that 3 people selected will include George but not Nina

A 5/56
B 9/56
C 15/56
D 21/56
E 25/56


OA C

Source: GMAT Prep

Solution:

We are given that 3 people are to be selected from 8 people and need to determine the probability that, of the 3 people selected, George is included but Nina is not. Let’s first determine the total number of ways to select 3 people from a group of 8.

The number of ways to select 3 people from a group of 8 is 8C3 = (8 x 7 x 6)/3! = 56.

Next, let’s determine the number of ways to select 3 people from a group of 8 when George is included but Nina is not.

Since George must be included and Nina is not, we can reduce the number of available spots from 3 to 2 (because George is already selected), and we can reduce the number of people available to be selected from 8 to 6 (Nina is not even considered, and George is already selected).

Thus, the number of ways to select 3 people when George is included and Nina is not is:

6C2 = (6 x 5)/2! = 15

So, finally, the probability of selecting a group of three with George and not Nina is:

15/56

Answer: C