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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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1024
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. the number of ways of their distribution $=4 \times 4 \times 4 \times 4 \times 4=4^{5}=1024$
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