In a class, there are 15 boys and 10 girls. Three students are selected at rando

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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:

Options:

A . 21 46

B . 25 117

C . 1 50

D . 3 25

Answer: Option A

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

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