- #1

AdityaDev

- 527

- 33

## Homework Statement

Consider a 11 digit positive integer formed by the digits 1,0 or both. The probability that no two zeros are adjacent is:

## Homework Equations

None

## The Attempt at a Solution

First digit has to be 1.

Total number of permutations=2

^{10}

Now 1XXXXXXXXXX is the format.

Taking 10 digits starting from 2nd digit, it has to be like 01X1X1X1X1 or it has to be like 1X1X1X1X1X.

(X can be 0 or 1).

For first case if I take one zero, it can be place in any of the 4 X = 4C1

If I take 2 zero, 4C2 and so one because the other X has to be filled by 1.

First case: 4c1+4c2+...+4c4=16

Second case:5c1+...5c5=32

Hence probability = (2

^{4}+2

^{5})/2

^{10}=3/64.

But answer is 9/64