Q.

A class has three teachers, Mr. P, Ms. Q, and Mrs. R and six students A,B,C,D,E,F. Number of ways in which they can be seated in a line of 9 chairs, if between any two teachers there are exactly two students, is k6! then the value of k is________ .

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answer is 18.

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Detailed Solution

Let T and S denote teacher and student, respectively. Then we have following possible patterns according to question:(i) TSSTSSTSS(ii) STSSTSSTS(iii) SSTSSTSSTHence, total number of arrangements are 3⋅(3!)6!=18×6!⇒ k=18
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