Question

(a) How many 12-bit strings contain exactly five 1's?

(b) How many 12-bit strings contain at least nine 1's?

.(c) How many 12-bit strings contain at least one 1?

(d) How many 12-bit strings contain at most one 1?

Answer 1

a) Total strings = C(12, 5) =

C(12, 5) because we need to select those 5 places where we are putting 1 and rest of the places will go with 0.

Total such strings = 792

b) At least nine 1's = (nine 1's) + (ten 1's) + (eleven 1's) + (Twelve 1s)

= 299

Hence total 299 such strings are possible.

c) At least one 1 = 2^12 - (no one) = 4096 - 1 = 4095

d) At most one 1 = (no 1s) + (one 1) =C(12,0) + C(12, 1) = 1 + 12 = 13

I hope these will help. Thank you.