First slide
Permutations
Question

A class has three teachers, Mr. R 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 k x 6!, then the value of k is ______.

Moderate
Solution

Let T and S denote teacher and student, respectively.

Then we have following possible patterns according to question:

(i) T S S T S S T S S

(ii) S T S S T S S T S

(iii) S S T S S T S S T

Hence, total number of arrangements are 3 . (3!)6! = 18 x 6!

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