Joan is allowed to invite 3 of her friends to join her on a family camping trip. If Joan has 10 friends, in how many way

[BTGmoderatorDC]

Joan is allowed to invite 3 of her friends to join her on a family camping trip. If Joan has 10 friends, in how many ways can she invite 3 of them?

A. 27
B. 120
C. 140
D. 360
E. 720


OA B

Source: Magoosh

[deloitte247]

Joan's Total Friends = 10
Friends to select = 3
Selecting 3 out of 10 friends $$10C_3=\frac{10!}{3!\left(10-3\right)}=\frac{10\cdot9\cdot8\cdot7!}{3!\cdot7!}=10\cdot3\cdot4=120$$
$$Answer\ \ is\ Option\ B$$

[Scott@TargetTestPrep]

Joan is allowed to invite 3 of her friends to join her on a family camping trip. If Joan has 10 friends, in how many ways can she invite 3 of them?

A. 27
B. 120
C. 140
D. 360
E. 720


OA B

Solution:

The order in which she invites her friends is of no consequence; hence, we will use combinations instead of permutations. The number of ways to invite 10 friends from 3 is:

10C3 = 10! / (3! x 7!) = (10 x 9 x 8) / 3! = 5 x 3 x 8 = 120.

Answer: B