Mathematics · Permutations and Combinations

JEE Advanced 2019 — Paper 2 — Question 30

Five persons A，B，C，D and E are seated in a circular arrangement．If each of them is given a hat of one of the three colours red，blue and green，then the number of ways of distributing the hats such that the persons seated in adjacent seats get different coloured hats is $\_\_\_\_$

Answer: 30

Numerical answer — enter this value.

Step-by-step solution

Maximum number of hats of same colour are 2 and minimum colour required are 3 .

So, the selection of hats will have to be of the type AABBC

${ }^{3} \mathrm{C}_{1}$ ways to select hat having single colour.

Then distribute that single hat in ${ }^{5} \mathrm{C}_{1}$ ways.

${ }^{2} \mathrm{C}_{1}$ ways to distribute hat to adjacent person, after that alternate coloured hat will be given so $3 \times 5 \times 2$ $=30$

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2019
Paper: Paper 2
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Circular Permutations