Question

Lidia is packing her suitcase in the dark, so as to not wake her little sister. She blindly chooses 3 of her 6 sweaters. What is the probability that she chooses her 3 favorite sweaters?

(Points : 3)
Option A: 1/216
Option B: 1/120
Option C: 1/20
Option D: 1/18

Answer 1

There are 6 choose 3 possibilities (combinations).
6C3 = 6!/(6-3)!3!
= 6•5•4/(3•2•1)
= 120/6
= 20
With 20 possibilities, there is a 1 in 20 chance that she will choose her favorite three.
The answer is Option C. 1/20.

Answer 2

The number of ways of choosing 3 objects from 6 objects is 6C3.

6C3 = 6!/[3!(6-3)!] = 6!/(3!3!) = 6*5*4/(3*2*1) = 20

This is the number of outcomes in the sample space. One of those outcomes will yield her 3 favorite sweaters.

So, the probability is 1/6C3 = 1/20

Therefore, the answer is Option 3.