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The number of binary strings of 17 zeros and 8 ones in which no two ones are adjacent is ___________

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The number of binary strings of 17 zeros and 8 ones in which no two ones are adjacent is ___________

(a) 43758

(b) 24310

(c) 32654

(d) 29803

This question was addressed to me by my college director while I was bunking the class.

I need to ask this question from Counting topic in chapter Counting of Discrete Mathematics

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Correct option is (a) 43758

Easiest explanation: First place 17 zeroes side by side _ 0 _ 0 _ 0 … 0 _ and 8 1’s can be placed in any of the (17+1) available gaps hence the number of ways  = ^n+1Ck = 43758.

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