A Probable Case
Probability
Level
2
Seven white balls and three black balls are placed in a line randomly, what is the probability that no two black balls are placed adjacently?
3/5
13/120
1/72
2/5
1/3
3/8
8/15
7/15
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1 solution
First, we find out the total number of possibilities, which is just 10!, so now we know that our denominator is going to be 10!, now, we find the numerator by first, finding the ways to place white balls, which is 7!, then, the black balls have 3 places to choose from out of 8,hence, 7! (8 C 3) , lastly, the black balls can arrange between themselves 6 times, hence, 7! 56*6/10!, which simplifies to 7/15!