Question

From a group of 3 Statisticians, 4 Economist and 4 Psychologist, a committee of 3 persons is to be selected. How many ways person can be selected
i. 2 Psychologist ii. At least 2 Economist

Answer 1

Given:

Number of statisticians (S)= 3

Number of economists (E)= 4

Number of Psychologist (P)= 4

To find:

Number of ways a committee of 3 people can be formed.

Solution:

1) Number of ways to select 2P = ⁴C₂ = 6

Number of ways to select one person out of 3S and 4E = ⁷C₁ = 7

Total number of ways = 6*7 = 42

2) Number of ways to select 2E = ⁴C₂ = 6

Number of ways of selecting one person from the remaining 2E, 3S and 4P:

= ⁹C₁ = 9

Total number of ways = 6*9 = 54

Therefore the answer is 42 and 54.