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Question

10 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!×8!
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B
10!×2!×3!×8!
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C
5!×2!×9!×8!
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D
10!×2!×8
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Solution

The correct option is D 10!×2!×8
There should be 3 students that has to be placed between 2 DCE students.
The DCE students can be arranged in 8 ways, i.e. at position (1,5),(2,6),(3,7),...(8,12)
and can interchange their places in 2! ways.
Now the rest IIT studentsa can be arranged in 10P10 ways
Total ways are 8×2!× 10P10=8×2!×10!


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