Question

$10$ mangoes are to be distributed among $5$ persons. The probability that at least one of them will receive none is :

• A. $\frac{35}{143}$
• B. $\frac{108}{143}$
• C. $\frac{18}{143}$
• D. $\frac{125}{143}$

Answer 1

The correct option is D $\frac{125}{143}$

10 mangoes can be distributed among 5 persons in

${}^{10+5-1}{C}_{5-1}{=}^{14}{C}_4$ ways

Therefore, Total number of elementary events =${}^{14}{C}_4$

Required probability

= 1 – probability that each person received at least

one mango

$⟹=1-\frac{{}^{10-1}{C}_{5-1}}{{}^{14}{C}_4}⟹1-\frac{{}^9{C}_4}{{}^{14}{C}_4}⟹=1-\frac{9!}{4!5!}\times \frac{4!10!}{14!}=1-\frac{18}{143}⟹=\frac{125}{143}$