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

The number of binary strings of 17 zeros and 8 ones in which no two ones are adjacent is ___________ Correct Answer 43758

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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