Arithmetic Ability
Permutations and Combinations

25 / 181

Q.

A box contains 5 green, 4 yellow and 5 white pearls. Four pearls are drawn at random. What is the probability that they are not of the same colour ? A) 11/91 B) 4/11 C) 1/11 D) 90/91

View Answer

Correct choice: D

Explanation:

Let S be the sample space. Then, n(s) = number of ways of drawing 4 pearls out of 14 = C414 ways = 14×13×12×11/4×3×2×1 = 1001 Let E be the event of drawing 4 pearls of the same colour. Then, E = event of drawing (4 pearls out of 5) or (4 pearls out of 4) or (4 pearls out of 5) ⇒C15+ C44+ C15 = 5+1+5 =11 P(E) = n(E)/n(S)=11/1001=1/91 Required probability = 1−1/91=90/91
25 / 181