Question

14. Out of 6 engineers and 4 doctors, how many groups of 4 professionals can be formed such that at
least 1 engineer is always there?
A. 129
B. 109
C. 229
D. 209​

Answer 1

Step-by-step explanation:

(D)

Explanation: There are four cases:

4 engineers = 6C4 = 15

3 engineers and 1 doctor = 6C3*4C1 = 20*4 = 80

2 engineers and 2 doctors = 6C2*4C2 = 15*6 = 90

1 engineer and 3 doctors = 6C1*4C3 = 24

Therefore, total number of ways = 15 + 80 + 90 + 24 = 209.