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Seven white balls and three black balls are randomly placed in a row, The probability that no two black balls are placed adjacently equals ?
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- 1/2
- 7/15
- 2/15
- 1/3
Correct Option: B
First we place seven white balls at places market W.
W -- W --W --W --W -- W -- W
If we place three black balls at -- places. Then no two black balls will be placed adjacently.
Total No, of -- places = 8
∴ No. of favourable ways for black balls = 8C3 = 8 x 7 x 6 / 1 x 2 x 3 = 56
Total no. of equally likely cases = 10! / 7!3!
= (10 x 9 x 8) / (1 x 2 x 3) = 15 x 8 = 120
∴ Reqd. Probability = 56 / 126 = 7/15
