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?
i)To distribute 3 prizes among 4 girls where no girl gets more than one prize the possible number of permutation possible are:4P3=24
ii) To distribute 3 prizes among 4 girls where a girl may get any number of prizes the number of possibilities are:4 × 4 × 4=64.
(since a prize can be given to any of the 4 girls.)
iii) To distribute 3 prizes among 4 girls where no girl gets all the prizes the number of possibilities are:(4 × 4 × 4)-(4)=64-4=60
(the situation where a single girl gets all the prizes has to reduced from the situation where a girl may get any number of prizes.)