How many bit strings of length 15 contain at least three 1s and at least three 0s?

Question

I need an answer to this question ASAP!

Answer 1

Hi,

first of all you know 2¹⁵ is all permutation

you don need some part such as:

String with no ones = 15!/(0!(15 - 0!)) = 1

String with no zeros = 15!/(0!(15 - 0!)) = 1

String with one one = 15!/1!(15 - 1!)=15

Strings with one zero = 15!/1!(15 - 1!)=15

Strings with two ones = 15!/2!(15 - 2!)=105

Strings with two zeros= 15!/2!(15 - 2!)=105

2¹⁵ - 1 - 1 - 15 - 15 - 105 - 105 = 32526 the number of strings.

I hope it is useful,

Minoo