Question

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 ?

Answer 1

four are drawn. so. p= total event /n
= 4/14 = 2/7

Answer 2

Let S be the sample space. Then,
n(s) = number of ways of drawing 4 pearls out of 14


= C414 ways = 14×13×12×114×3×2×1= 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)=111001=191



Required probability =
$1 - \frac{1}{91} \\ = \frac{90}{91}$