How many bit strings of length 14 have: (a) Exactly three 0s? (b) The same number of 0s as 1s? (d) At least three 1s?
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(a) Exactly three 0s means other digits are always one, so the number of permutations would be equal to . Answer is 2184.
(b) Since it's a bit string of 14 digits and there can be only digits 0 or 1, we need to select 7 0s and the rest would be 7 1s, so the number of permutations would be equal to . The answer is 17297280.
(c) The answer would be similar to question a, but here the rest of the digits can be either 0 or 1, so it would have to be multiplied by because there 11 digits and each one of them can be either of two choices. . Answer is 4472832.