BITSTRING LENGTH QUESTION How many bitstrings of length 19 a

BITSTRING LENGTH QUESTION

How many bitstrings of length 19 are there that have an even number of ones in them? Your answer must be a short simple expression, not a sum of many terms for full credit.

Solution

No of bitstring with exactly 2 1s = c(19,2)

=19!(2!(192)!)=19!(2!(192)!)

= 171

No of bitstring with exactly 4 1s = c(19,4) etc

Total combination = 19c2+19c$+19c6+….+19C18

However the simple way way of attending it would be 2¹⁸-1 = 262143