If Quantity A is the number of ways to assign a number from 1 to 5 without repetition to each of four people, and Quantity B is the number of ways to assign a number from 1 to 5 without repetition to each of 5 people, then which of the following statements is correct with respect to Quantities A and B?

Correct option is C

Given:

Quantity A: Number of ways to assign a number from 1 to 5 without repetition to each of four people.

Quantity B: Number of ways to assign a number from 1 to 5 without repetition to each of five people.

Solution:

For Quantity A (assigning numbers to 4 people):
We choose a distinct number for each of the 4 people, and there are 5 available numbers. The number of ways to do this is a permutation of 5 items taken 4 at a time:

P(5, 4) =$$\frac{5!}{(5-4)!} = \frac{5!}{1!} = 5 \times 4 \times 3 \times 2 = 120$$​

For Quantity B (assigning numbers to 5 people):
We assign a distinct number to each of the 5 people, so it's a permutation of 5 items taken 5 at a time:

P(5, 5) $$= \frac{5!}{(5-5)!} = \frac{5!}{0!} = 5! = 120$$​
Both Quantity A and Quantity B result in the same number of ways, which is 120.