Question

How many bit strings of length 15 contain exactly 3 zeros?

Answer 1

To find the number of bit strings of length 15 that contain exactly 3 zeros, we can use the concept of combinations. The total number is 455.

Step-by-step explanation:

To find the number of bit strings of length 15 that contain exactly 3 zeros, we can use the concept of combinations. We have 15 positions in the string and we need to choose 3 of them to be zeros. The remaining 12 positions will be filled with ones.

1. First, we calculate the number of ways to choose 3 positions out of 15. This can be done using the combination formula C(15, 3) = 15! / (3! * (15-3)!).
2. Next, we fill the chosen 3 positions with zeros and the remaining 12 positions with ones. We have only one choice for the zeros and ones, so the number of possibilities is 1.

Therefore, the total number of bit strings of length 15 that contain exactly 3 zeros is C(15, 3) * 1 = 455.