Question:
There are \(5\) boys and \(3\) girls seated in a row for a photograph. The number of ways in which a photograph can be taken if the girls occupy only odd places is...
There are \(5\) boys and \(3\) girls seated in a row for a photograph. The number of ways in which a photograph can be taken if the girls occupy only odd places is...
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There are 4 odd positions among 8 seats. Place girls first, then boys.
Updated On: Oct 1, 2026
- \(5040\)
- \(2880\)
- \(720\)
- \(40320\)
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Count the odd places
In a row of \(8\) seats the odd places are \(1,3,5,7\). So there are \(4\) odd places.
Step 2: Place the girls
The \(3\) girls choose \(3\) of these \(4\) places in order: \({}^4P_3=4\times3\times2=24\) ways.
Step 3: Place the boys
The \(5\) boys fill the remaining \(5\) seats in \(5!=120\) ways.
Step 4: Multiply
\[ 24\times120=2880 \]
Final Answer:
The number of arrangements is \(2880\), option (B). \[ \boxed{\text{(B) }2880} \]
In a row of \(8\) seats the odd places are \(1,3,5,7\). So there are \(4\) odd places.
Step 2: Place the girls
The \(3\) girls choose \(3\) of these \(4\) places in order: \({}^4P_3=4\times3\times2=24\) ways.
Step 3: Place the boys
The \(5\) boys fill the remaining \(5\) seats in \(5!=120\) ways.
Step 4: Multiply
\[ 24\times120=2880 \]
Final Answer:
The number of arrangements is \(2880\), option (B). \[ \boxed{\text{(B) }2880} \]
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