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Question

Seven white balls and three black balls are randomly arranged in a row. The probability that no two black balls are placed adjacently is

A
12
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B
715
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C
215
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D
13
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Solution

The correct option is D 715
Total ways of arranging balls =10!7!3!
Arranging such that no two black balls are together 1st arrange 7 white balls in 7!7!=1 ways .
Now, we have 8 places when we can keep those balls.
no. of ways =1.8C3=8!3!5!
P (no. black ball together) =8!3!5!10!7!3!

=8!3!5!×7!×3!10!

=8!×7×6×5!5!×10×9×8!

=4290

=715

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