Question

There are six teachers. Out of them two are primary teachers, two are middle teachers and two secondary teachers. They are to stand in a row, so as the primary teacher, middle teachers and secondary teachers are always in a set. The number of ways in which they can do so, is

Answer 1

There are $2$ primary teacher.

They can stand in a row in $P(2,2)$ $=2!=2\times 1$ ways $=2$ ways.

There are $2$ secondary teachers. They can stand in row in $P(2,2)=2!=2\times 1$ ways $=2$ ways.

These three sets can be arranged in themselves in $3!=3\times 2\times 1=6$ ways.

Hence the required number of ways $2\times 2\times 2\times 6=48.$