# 5.(a)  Out of    students, two sections of and are formed. If you and your friend are among the students, what is the probability that(a) you both enter the same section?

H Harsh Kankaria

Total number of students = 100

Let A and B be the two sections consisting of 40 and 60 students respectively.

Number of ways of selecting 2 students out of 100 students.=

(a)

If both are in section A:

Number of ways of selecting 40 students out of 100 =   (The remaining 60 will automatically be in section B!)

Remaining 38 students are to be chosen out of (100-2 =) 98 students

Required probability if they both are in section A =

Similarly,

If both are in section B:

Number of ways of selecting 60 students out of 100 =   (The remaining 40 will automatically be in section A!)

Remaining 58 students are to be chosen out of (100-2 =) 98 students

Required probability if they both are in section B =

Required probability that both are in same section = Probability that both are in section A + Probability that both are in section B

=

Hence, the required probability that both are in same section is

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