**Question:**

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?

**Solution:**

(i)To distribute 3 prizes among 4 girls where no girl gets more than one prize the possible number of permutation possible are: ${ }^{4} \mathrm{P}_{3}=24$

(ii) To distribute 3 prizes among 4 girls where a girl may get any number of prizes the number of possibilities are: $4 \times 4 \times 4=64$.

(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: $(4 \times 4 \times 4)-(4)=64-4=60$

(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.)