Question

There are two letters C and D. If repetitions such as CC are permitted, how many permutations are possible?

A) 1

B) 0

C) 4

Answer 1

To find the number of permutations with the letters C and D where repetitions are allowed, we multiply the number of choices for each of the two positions. There are 2 choices for each position, yielding 2 x 2 = 4 possible permutations: CC, CD, DC, and DD.

Step-by-step explanation:

The question is about determining the number of permutations possible with two letters (C and D), where repetitions such as CC are allowed. In this case, since there are two different spots where each of the two letters can go, we can think of it as a two-step process:

1. Choose a letter for the first spot (2 choices: C or D)
2. Choose a letter for the second spot (again, 2 choices: C or D)

Since the choices are independent, we can multiply the number of choices for each step together to find the total number of permutations:

2 choices (for the first spot) × 2 choices (for the second spot) = 4 permutations.

Therefore, there are 4 possible permutations: CC, CD, DC, DD.

The correct answer to the question is C) 4.