Question

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 bwteen any two teachers there are exactly two students, is

• A. $18(6!)$
• B. $12(6!)$
• C. $24(6!)$
• D. $6(6!)$

Answer 1

The correct option is A $18(6!)$

We have,

A class has three teachers Mr. $X$, Ms. $Y$, Mrs.$Z$

Students $=A,B,C,D,E,F$

Total chairs $=9$

Let the teachers$=T$

And the students$=S$

Now, According to question

Arrange

$TSS,TSS,TSS=3!\times 6!$

$SST,SST,SST=3!\times 6!$

$STS,STS,STS=3!\times 6!$

Then, total number of ways,

$3\times 3!\times 6!$

$18(6!)$

Hence, this is the answer.