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A class has three teachers, Mr. X, Ms. Y and Mrs. Z 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 x. Then $\frac{x}{10}$ is

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answer is 1296.

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Detailed Solution

The possible arrangements of teachers and students
can be as follows :
(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 ways $= 3 \cdot (3!) 6! == (18) 6!$

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