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There are five boys A, B, C, D and E. Th...

There are five boys A, B, C, D and E. The order of their height is `A lt B lt C lt D lt E`. Number of ways in which they have to be arranged in four seats in increasing order of their height such that C and E are never adjacent.

Text Solution

Verified by Experts

The correct Answer is:
4
Case I : When exactly one of C and E is selected
Number of ways of selecting one of C and E is `.^(2)C_(1)`.
For any one of them selected there is only one way of arranging him with A, B, D.
So, number of arrangements are `.^(2)C_(1)xx1=2`
Case II : When both are selected
When both are selected, D must be selected. The remaining one may be A or B.
So, number of ways of arrangements are `.^(2)C_(1)xx1=2`
So, total number of ways =4
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