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If a group of six students including two particular students A and B stand in a row, then the probability of getting an arrangement in which A and B are separated by exactly one student in between them is
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$\frac{4}{15}$
No. of ways to arrange 6 students in row $=6$ !
Consider group of 3 students consisting $A$ and $B$ with 1 boy. Now there are 4 things to be arranged.
No. of ways $=4 ! 2 ! \times{ }^4 C_1$
Probability $=\frac{{ }^4 C_1 \times 4 ! \times 2 !}{6 !}=\frac{4}{15}$
Consider group of 3 students consisting $A$ and $B$ with 1 boy. Now there are 4 things to be arranged.
No. of ways $=4 ! 2 ! \times{ }^4 C_1$
Probability $=\frac{{ }^4 C_1 \times 4 ! \times 2 !}{6 !}=\frac{4}{15}$
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