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In how many ways can 10 different prizes...

In how many ways can 10 different prizes be given to 5 students if one particular boy must get 4 prizes and rest of the students can get any number of prizes?

Text Solution

Verified by Experts

The correct Answer is:
860160
The number of selections of 4 prizes to the particular boy is `.^(10)C_(4)`. From the remaining 6 prizes, each prize can be given to any of the four students. Therefore, the number of ways is `4^(6)`.
Therefore, the total number of ways is
`.^(10)C_(4)xx4^(6)=210xx4096=860160`.
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