Question

In a school, there are 10 math teachers and 8 chemistry teachers. If four teachers are to be selected for a program randomly, then what is the probability that 2 math and 2 chemistry teachers are selected?

A. \(1250\over3060\)

B.\(1260\over3060\)

C.\(1261\over3060\)

D. \(7\over17 \)

1. Only A
2. Only B
3. Only C
4. Both B and D

Answer 1

Correct Answer - Option 4 : Both B and D

Given:

Math teachers: 10

Chemistry teachers: 8

Formula used:

nCr = n!/((n-r)! × r!)

P = (Number of favorable outcomes)/(Total number if outcomes)

Calculation:

Total teachers: 10 + 8 = 18

The number of ways of selecting 4 teachers among all: 

\(18C4\) = 3060

Combination of selecting 2 math teachers and 2 chemistry teachers:

\(10C2\times8C2\) = 1260

Probability:

⇒  \(1260\over3060\) 

⇒  \(7\over17 \)

∴ Both B and D is the correct answer.