Question:
In how many ways can $5$ prizes be distributed among $4$ boys when every boy can take one or more prizes ?
In how many ways can $5$ prizes be distributed among $4$ boys when every boy can take one or more prizes ?
Updated On: Jun 18, 2022
- 1024
- 625
- 120
- 600
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The Correct Option is A
Solution and Explanation
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
$= 4 \times 4 \times 4 \times 4 \times 4 = 4^5 = 1024$
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
$= 4 \times 4 \times 4 \times 4 \times 4 = 4^5 = 1024$
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Concepts Used:
Permutations
A permutation is an arrangement of multiple objects in a particular order taken a few or all at a time. The formula for permutation is as follows:
\(^nP_r = \frac{n!}{(n-r)!}\)
nPr = permutation
n = total number of objects
r = number of objects selected
Types of Permutation
- Permutation of n different things where repeating is not allowed
- Permutation of n different things where repeating is allowed
- Permutation of similar kinds or duplicate objects