MHTCET 13 May 2023 Shift 1 Solved Paper

There are 5 caps and 3 colours.
∴‌‌ At least one colour will get repeated.
As adjacent caps should be of different colours, no colour can repeat thrice.
∴‌‌ Exactly two colours will repeat twice.
∴‌‌ Colour of the caps are selected in 3 ways as follows:
Red-Red-Green-Green-Blue,
Red-Red-Green-Blue-Blue,
Red-Green-Green-Blue-Blue.
Now, while distributing the caps from above combinations, we choose any one of the 5 persons and give single colour cap. And remaining four caps can be distributed in alternate colour sequence, clock-wise or anticlock-wise.
This can be done in 5×2 ways.
∴‌‌ Required number of ways =3×5×2=30.