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In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:

/ Aptitude, Probability / By
Question:
In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:

[A].

21
46

[B].

25
117

[C].

1
50

[D].

3
25

Answer: Option A

Explanation:

Let S be the sample space and E be the event of selecting 1 girl and 2 boys.

Then, n(S) = Number ways of selecting 3 students out of 25
= 25C3 `
= (25 x 24 x 23)
(3 x 2 x 1)
= 2300.
n(E) = (10C1 x 15C2)
= 10 x (15 x 14)
(2 x 1)
= 1050.
P(E) = n(E) = 1050 = 21 .
n(S) 2300 46