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A class has tree 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 l

Monjur Alahi

A class has tree 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
A. `18xx6!`
B. `12xx6!`
C. `24xx6!`
D. `6xx6!`


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Salim Ahmed Kawsar

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Correct Answer - A
`(a)` 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*(3!)6!=(18)6!`

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