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Question

Ten IIT and 2 DCE students sit in a row. The number of ways in which exactly 3 IIT students sit between 2 DCE students is

A
10C3×2!×3!×8!
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B
10!×2!×3!×8!
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C
5!×2!×9!×8!
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D
None of these
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Solution

The correct option is A 10C3×2!×3!×8!
Three IIT students who will be between the IIT students can be selected in 10C3 ways.
Now, two DCE students having three IIT students between them can be arranged in 2!×3! ways.
Finally, a group of above five students and the remaining seven students together can be arranged in 8! ways.
Hence, total number of ways is 10C3×2!×3!×8!

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