In how many ways can 3 prizes be distributed among 4 girls, when (i)

1.	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) 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.)

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) 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.)

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