7 persons, among whom are A and B, stand in a line
for a photograph. Find the probability that there are
exactly 2 persons between A and B.
Answers
Given : 7 persons, among whom are A and B, stand in a line for a photograph.
To Find : the probability that there are exactly 2 persons between A and B.
Solution:
7 person can stand in 7! = 5040 ways
A and B can stand in 8 ways if there are exactly 2 persons between A and B
positions of (A , B)
( 1 , 4) , ( 4 , 1) , ( 2 , 5) , ( 5 , 2) , ( 3 , 6) , ( 6, 3) , ( 4 , 7) , (7, 4)
and remaining 5 persons can stand in 5! = 120 ways
Hence 8 * 5! ways
= 8 *1 20 = 960
probability that there are exactly 2 persons between A and B.
= 8 * 5! / 7!
= 8/ (7 * 6)
= 8/42
= 4/21
= 0.1905
probability that there are exactly 2 persons between A and B. is 4/21
or 0.1905
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