In how many ways can 3 prizes be distributed among 4 girls, when
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.)
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
- 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.)
- 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.)