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  4. In how many ways can 5 prizes be distributed among four students when every student can take one or more prizes?

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Q. In how many ways can $5$ prizes be distributed among four students when every student can take one or more prizes?

BITSATBITSAT 2011

Solution:

From the problem, each prize can be distributed to anyone of those four students.
So, we may say required number of ways $=4^{5}=2^{10}=1024$