Question

Find the number of bit strings that satisfies the given conditions. The bit strings of length 11 having at least four 1s

Answer 1

To find the number of bit strings of length 11 that have at least four 1s, we can use combinations. We sum up the combinations for choosing different numbers of 1s in the bit string.

Step-by-step explanation:

To find the number of bit strings of length 11 that satisfy the condition of having at least four 1s, we can use the concept of combinations. We need to consider the number of ways to choose positions for the 1s, since the remaining positions will contain 0s.

1. Choose 4 positions for the 1s: C(11, 4)
2. Choose 5 positions for the 1s: C(11, 5)
3. Choose 6 positions for the 1s: C(11, 6)
4. Choose 7 positions for the 1s: C(11, 7)
5. Choose 8 positions for the 1s: C(11, 8)
6. Choose 9 positions for the 1s: C(11, 9)
7. Choose 10 positions for the 1s: C(11, 10)
8. Choose 11 positions for the 1s: C(11, 11)

Finally, sum up all the combinations to find the total number of bit strings:

Total = C(11, 4) + C(11, 5) + C(11, 6) + C(11, 7) + C(11, 8) + C(11, 9) + C(11, 10) + C(11, 11)