10 mangoes are to be distributed among 5 persons. The probability that at least one of them will receive none, is
Answer & explanation
Correct answer: option 4
10 mangoes can be distributed among 5 persons in ${^{10+5-1}C}_{5-1}={^{14}C}_4$ ways.
Total number of elementary events = ${^{14}C}_4$
Required probability =1 - Probability that each person receives at least one mango
$=1-\frac{^{10-1}C_{5-1}}{^{14}C_4}=1-\frac{^9C_4}{^{14}C_4}=1-\frac{18}{143}=\frac{125}{143}$