Question:
The number of ways in which first, second and third prizes can be given to $5$ competitors is
The number of ways in which first, second and third prizes can be given to $5$ competitors is
Updated On: Jun 27, 2024
- 10
- 60
- 15
- 125
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The Correct Option is B
Solution and Explanation
First prize can be given in $5$ ways. Then second prize can be given in $4$ ways and the third prize in $3$ ways (Since a competitior cannot get two prizes) and hence the no. of ways. = $5 \times 4 \times 3 = 60$ ways
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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