Carol is having friends over to watch home movies. She has 6 reels of

Carol is having friends over to watch home movies. She has 6 reels of home movies, but she and her friends have time to watch only 3 of them. Carol must decide which reels to watch and in what order. How many different orderings does Carol have from which to choose?

A. 120
B. 96
C. 60
D. 36
E. 20

Solution :

When order matters we apply the Permutation Method 

6P3   = 6 * 5 * 4 = 120 ways

Option A

To determine the number of different orderings that Carol can choose, we need to use the concept of permutations.

Carol has 6 reels of home movies, but she can only watch 3 of them. The number of different orderings can be calculated using the formula for permutations of n objects taken r at a time, which is given by:

P(n, r) = n! / (n - r)!

Where n is the total number of objects (reels) and r is the number of objects (reels) to be chosen.

In this case, Carol has 6 reels and she needs to choose 3 of them. So the calculation becomes:

P(6, 3) = 6! / (6 - 3)!
= 6! / 3!
= (6 * 5 * 4 * 3 * 2 * 1) / (3 * 2 * 1)
= 6 * 5 * 4
= 120

Therefore, Carol has 120 different orderings to choose from.

The correct answer is A. 120.