Question:
The number of ways in which 5 girls and 3 boys can be seated in a row so the no two boys are together is
The number of ways in which 5 girls and 3 boys can be seated in a row so the no two boys are together is
Updated On: Apr 18, 2024
- 14040
- 14440
- 14000
- 14400
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The Correct Option is D
Solution and Explanation
5 girls can be arranged in $5 !=120$ ways
3 boys between 5 girls with positions can be arranged in ${ }^{6} P _{3}=6 \cdot 5 \cdot 4=120$ ways
$\therefore$ Total number of arrangements $=120 \times 120=14400$
3 boys between 5 girls with positions can be arranged in ${ }^{6} P _{3}=6 \cdot 5 \cdot 4=120$ ways
$\therefore$ Total number of arrangements $=120 \times 120=14400$
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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