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  4. In how many ways can 5 prizes be distributed among 4 boys when every boy can take one or more prizes ?

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Q. In how many ways can $5$ prizes be distributed among $4$ boys when every boy can take one or more prizes ?

BITSATBITSAT 2012

Solution:

First prize may be given to any one of the $4$ boys, hence first prize can be distributed in $4$ ways.
similarly every one of second, third, fourth and fifth prizes can also be given in $4$ ways.
$\therefore $ the number of ways of their distribution
$= 4 \times 4 \times 4 \times 4 \times 4 = 4^5 = 1024$