Question

The Principal wants to arrange 5 students on the platform such that the boy SALIM occupies the second position and such that the girl. SITA is always adjacent to the girl RITA. How many such arrangements are possible?

Answer 1

Let the five seats be arranged as shown below.
`underset (square )(I)" "underset(S)(II) " "underset(square)(III)" "underset(square)(IV)" "underset(square)(V)`
Keep Sajal fixed at the second position.
Since Tanvy and Aditi are ot sit together, none of them can occupy the first seat.
The first seat can be occupied by any of the two remaining students in `2! =2` ways.
Number of ways in which 2 seats namely III, IV or IV, V may be occupied by Tanvy and Aditi `=(2!)+(2!)=(2+2)=4.`
The remaining seat may now be occupied bya the 5th student in 1 way only.
Hence, the required number of arrangement `=(2xx4xx1)=8.`