JEE Advanced · 2019 · 27 May 2019 · Paper 2 · Permutations and Combinations

WhatsApp Email

Five person A,B,C,D and E are seated in a ciruclar 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

Solution

For a circular arrangement of 5 people with 3 colors where adjacent people must have different colors, we use chromatic polynomial considerations. The valid colorings have the pattern: 1 person of one color, 2 of another, 2 of the third. For example, 1R, 2B, 2G: there are

^{5} C_{1} \times 2 = 10

ways (choose position for R, then arrange B and G). Similarly for 1B, 2R, 2G and 1G, 2R, 2B. Total:

3 \times 10 = 30

JEE Advanced · 2019 · 27 May 2019 · Paper 2 · Numerical answer

Practise more: all JEE Advanced PYQs on Permutations and Combinations →

More JEE Advanced questions on Permutations and Combinations

The number of ways to distribute 10 identical red pens and 14 identical blue pens among four persons such that each person gets 6 pens, is ____.
JEE Advanced 2026View solution →
Let $S$ be the set of all seven-digit numbers that can be formed using the digits 0,1 and 2 . For example, 2210222 is in $S$ , but 0210222 is NOT in $S$ .

Then the number of elements $x$ in $S$ such that at least one the digits 0 and 1 appears exactly twice in $x$ , is …
JEE Advanced 2025View solution →
Let $S = {1, 2, 3, 4, 5, 6}$ and $X$ be the set of all relations $R$ from $S$ to $S$ that satisfy both the following properties.
i. $R$ has exactly 6 elements.
ii. For each $(a, b) \in R$ , we have $∣ a - b ∣ \geq 2$ .
Let $Y = {R \in X$ : The range of $R$ has exactly one element $}$ and …
JEE Advanced 2024View solution →
Let $S = {1, 2, 3, 4, 5, 6}$ and $X$ be the set of all relations $R$ from $S$ to $S$ that satisfy both the following properties.
i. R has exactly 6 elements.
ii. For each $(a, b) \in R$ , we have $∣ a - b ∣ \geq 2$ .

Let $Y = {R \in X$ : The range of R has exactly one element $}$ and …
JEE Advanced 2024View solution →
A group of 9 students, $s_{1}, s_{2}, \dots .., s_{9}$ , is to be divided to from three teams X, Y, and Z of sizes 2, 3, and 4, respectively. Suppose that $s_{1}$ cannot be selected for the team X, and $s_{2}$ cannot be selecte …
JEE Advanced 2024View solution →
The number of 4-digit integers in the closed interval [2022, 4482] formed by using the digits $0, 2, 3, 4, 6, 7$ is ____.
JEE Advanced 2022View solution →