Six people A,B,C,D,E,F are going to sit in a row on a bench. Let A and B are to be adjacent. C does not want to sit adjacent to D. E and F can sit anywhere. Number of ways in which these six people can be seated, is:

Question

Six people A,B,C,D,E,F are going to sit in a row on a bench.  Let A and B are to be adjacent.  C does not want to  sit adjacent to D. E and F can sit anywhere. Number of ways in which these six people can be seated, is:

Infinity Learn · Accepted Answer

Consider AB as one unit. C and D are to be separated; E and F any where AB and E, F can be seated in a row in $$3$$! x $$2$$! ways No. of gaps between AB, E, F is  $$4$$ □ AB □ E □ F □ In those $$4$$ gaps C,D can be seated in $$C2$$   $$4$$ x $$2$$! ways Total number of ways $$=$$ $$3$$! $$x2$$! x $$C2$$  $$4x$$ $$2$$!$$=144$$

$Six people A,B,C,D,E,F are going to sit in a row on a bench. Let A and B are to be adjacent. C does not want to$ $sit adjacent to D . E and F can sit anywhere. Number of ways in which these six people$ can be seated, is:

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