Question

How many 16-bit strings contain at least thirteen 1’s?

Answer 1

To find the number of 16-bit strings that contain at least thirteen 1's, we can use combinatorics. The total number of 16-bit strings that contain at least thirteen 1's is 697.

Step-by-step explanation:

To find the number of 16-bit strings that contain at least thirteen 1's, we can use combinatorics. Since we want at least thirteen 1's, we can have any number of 1's ranging from thirteen to sixteen. We can calculate this by summing up the number of possibilities for each case:

1. Case 1: 13 1's and 3 0's - There are 16 choose 13 ways to arrange the 1's, which is equal to 560.
2. Case 2: 14 1's and 2 0's - There are 16 choose 14 ways to arrange the 1's, which is equal to 120.
3. Case 3: 15 1's and 1 0 - There are 16 choose 15 ways to arrange the 1's, which is equal to 16.
4. Case 4: 16 1's and 0 0's - There is only 1 way to arrange all 1's.

Therefore, the total number of 16-bit strings that contain at least thirteen 1's is 560 + 120 + 16 + 1 = 697.