Question

There are only two women among 20 persons taking part in a pleasure trip. The 20 persons are divided into two groups, each group consisting of 10 person. Then the probability that the two women will be in the same group is `9//19` b. `9//38` c. `9//35` d. none
A. `9//19`
B. `9//38`
C. `9//35`
D. none of these

Answer 1

Correct Answer - A
The number of ways in which 20 people can be divided into two equal group is
`n(S) = (20!)/(10! 10! 2!)`
The number of ways in which 18 people can be divided into groups of 10 and 8 is
`n(E) = (18!)/(10! 8!)`
`therefore P(E) = (18!)/(10! 8!) (10! 10! 2)/(20!) = (10 xx 9 xx 2)/(20 xx 19) = (9)/(19)`