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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

Verified Answer :

djsdoodle

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.

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

6C3 = 6!/[3!(6-3)!] = 6!/(3!3!) = 654/(321) = 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.

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