Question

The bit strings of length 11 having at least four 1s:

A) 330
B) 462
C) 495
D) 660

Answer 1

The number of bit strings of length 11 having at least four 1s is 1023.

Step-by-step explanation:

The number of bit strings of length 11 that have at least four 1s can be found using the concept of combinations. Let's break it down step by step:

1. Calculate the number of bit strings of length 11 with exactly four 1s: C(11, 4) = 11! / (4! * (11 - 4)!) = 330.
2. Calculate the number of bit strings of length 11 with exactly five 1s: C(11, 5) = 11! / (5! * (11 - 5)!) = 462.
3. Calculate the number of bit strings of length 11 with exactly six 1s: C(11, 6) = 11! / (6! * (11 - 6)!) = 462.
4. Calculate the number of bit strings of length 11 with exactly seven or more 1s: C(11, 7) + C(11, 8) + C(11, 9) + C(11, 10) + C(11, 11) = 462 + 330 + 165 + 55 + 11 = 1023.

Therefore, the total number of bit strings of length 11 with at least four 1s is 1023.