Question:
The number of ways in which $5$ boys and $5$ girls can be seated for a photograph so that no two girls sit next to each other is
The number of ways in which $5$ boys and $5$ girls can be seated for a photograph so that no two girls sit next to each other is
Updated On: Oct 7, 2023
- $6 \,! \,5 \,!$
- $(5\,!)^2$
- $\frac{10\,!}{(5\,!)}$
- $\frac{10\,!}{(5\,!)^2}$
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The Correct Option is A
Solution and Explanation
The correct option is(A): 6!5!.
\(X.X.X.X.X.\) First place \(5\) boys at the \(X\) places. This can be done in \(5!\). Since no two girls sit next to each \(\therefore\) we can give them seats at places marked by This can be done in \(^{6}p_{5}\) ways. \(=6\times5\times4\times3\times2=6!\) ways. \(\therefore\) reqd. number of ways \(= 6! \,5!\)
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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