In how many ways can 3 prizes be distributed among 4 girls, when
(i) no girl gets more than one prize?
(ii) a girl may get any number of prizes?
(iii) no girl gets all the prizes?

Answer

(i) 24 (ii) 64 (iii) 60

Explanation

(i) The 1st prize can be given to anyone of the 4 girls in 4 ways.
Similarly, the second prize can be given in 3 ways and the 3rd prize can be given in 2 ways.
`therefore " the required number of ways"=(4xx3xx2)=24.`
(ii) 1st prize can be given in 4 ways, 2nd prize can be given in 4 ways and the 3rd prize can be given in 4 ways.
`therefore " the required number of ways"=(4xx4xx4)=64.`
(iii) Number of ways in which a girl does not get all the prizes = (number of ways in which a girl may get any number of prizes) - (number of ways in which a girl gets all the prizes)
`=(64-4)=60.`