To solve this problem, we need to consider two scenarios: A and B are at the ends of the line, and A and B are not at the ends of the line.

1. If A and B are at the ends of the line, there are 2 ways to arrange A and B (A at the left end and B at the right end, or vice versa). The remaining 8 people can be arranged in 8! ways. So, there are 2*8! arrangements in this case.

2. If A and B are not at the ends of the line, there are 6 positions where we can place them (with 3 people in between). For each of these positions, there are 2 ways to arrange A and B. The remaining 8 people can be arranged in 8! ways. So, there are 6*2*8! arrangements in this case.

So, the total number of arrangements where there are exactly 3 people between A and B is 2*8! + 6*2*8!.

The total number of arrangements of 10 people is 10!.

So, the probability that there are exactly 3 people between A and B is (2*8! + 6*2*8!) / 10! = 4/15.

So, the answer is (b) 4/15.

Question

To solve this problem, we need to consider two scenarios: A and B are at the ends of the line, and A and B are not at the ends of the line.

1. If A and B are at the ends of the line, there are 2 ways to arrange A and B (A at the left end and B at the right end, or vice versa). The remaining 8 people can be arranged in 8! ways. So, there are 2*8! arrangements in this case.

2. If A and B are not at the ends of the line, there are 6 positions where we can place them (with 3 people in between). For each of these positions, there are 2 ways to arrange A and B. The remaining 8 people can be arranged in 8! ways. So, there are 6*2*8! arrangements in this case.

So, the total number of arrangements where there are exactly 3 people between A and B is 2*8! + 6*2*8!.

The total number of arrangements of 10 people is 10!.

So, the probability that there are exactly 3 people between A and B is (2*8! + 6*2*8!) / 10! = 4/15.

So, the answer is (b) 4/15.

Knowee AI · Accepted Answer

To solve this problem, we need to consider two scenarios: A and B are at the ends of the line, and A and B are not at the ends of the line.

1. If A and B are at the ends of the line, there are 2 ways to arrange A and B (A at the left end and B at the right end, or vice versa). The remaining 8 people can be arranged in 8! ways. So, there are 2*8! arrangements in this case.

2. If A and B are not at the ends of the line, there are 6 positions where we can place them (with 3 people in between). For each of these positions, there are 2 ways to arrange A and B. The remaining 8 people can be arranged in 8! ways. So, there are 6*2*8! arrangements in this case.

So, the total number of arrangements where there are exactly 3 people between A and B is 2*8! + 6*2*8!.

The total number of arrangements of 10 people is 10!.

So, the probability that there are exactly 3 people between A and B is (2*8! + 6*2*8!) / 10! = 4/15.

So, the answer is (b) 4/15.

If 10 men, among whom are A and B, stand in a row, what is the probabilitythat there will be exactly 3 men between A and B ?(a) 11/15(b) 4/15(c) 1/15(d) 2/15

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