Q

A small store has five units of a new phone model in stock: two white, two black, and one red. Three customers arrive at the shop to buy a unit each. Each one has a pre-determined choice of the colour and will not buy a unit of any other colour. All the three customers are equally likely to have chosen any of the three colour. What is the probability that the store will be able to satisfy all the three customers?

A. \(\frac{4}{5}\)

B. \(\frac{7}{9}\)

C. \(\frac{2}{3}\)

D. \(\frac{8}{9}\)

E. \(\frac{1}{3}\)

C. \(\frac{2}{3}\)

White = 2 Black = 2 Red = 1

All three customers has three choices i.e. W,B,R

\(\Rightarrow\) Total combination possible is 3 × 3 × 3 = 27

\(\Rightarrow\) Combination not possible are given below

WWW – 1

BBB – 1

RRR – 1

RRB – \(\frac{3!}{2!}\) = 3

RRW – \(\frac{3!}{2!}\) = 3

So total = 9

P = \(\frac{27-9}{27}\)

= \(\frac{2}{3}\)