Question

The principal wants to arrange

5

students on the platform such that the boy 'SALIM' occupies the second position and the girl 'RUNA' is always adjacent to the girl 'MONA. How may such arrangements are possible.

Accepted Answer

Given conditions:

The first position is not specified, so any of the five students could be placed there.

Salim, a boy, must be in the second position.

Runa, a girl, must be adjacent to Mona, who is also a girl. This means that either Runa could be in the first or third position and Mona would be in the fourth position or vice versa.

Using these conditions, we can consider the following cases:

If Runa is in the first position, Mona is in the fourth position.

There are two possible girls who could be in the first position.

Salim must be in the second position.

There are two possible girls who could be in the third position.

The last position can be filled by any of the remaining two students.

So, the total number of arrangements in this case is $2 \times 1 \times 2 \times 2 = 8 .$

Hence, the required answer is obtained.

The principal wants to arrange $5$ students on the platform such that the boy 'SALIM' occupies the second position and the girl 'RUNA' is always adjacent to the girl 'MONA. How may such arrangements are possible.

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