In how many ways can 4 red, 3 yellow and 2 green chairs be arranged in a row if the chairs of the same colour are indistinguishable?a)15120b)1260c)362880d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Total no of balls = 9
red balls = 4
yellow balls = 3
green balls = 2
Total no. of arrangements = 9!/(4!*3!*2!)
= 1260

Answer

You'll have to use permutation and combination formula that is the number of Total items factorial divide by number of items repeating factorial in this case it is 9 factorial divide by 4 factorial into 3 factorial into 2 factorial it will give you the answer 1260

Answer

Helpp

Answer

We are given 4 red chairs, 3 yellow chairs, and 2 green chairs. We need to find the number of ways these chairs can be arranged in a row if the chairs of the same color are indistinguishable.

To solve this problem, we can use the concept of permutations. Permutations are arrangements of objects in a specific order. In this case, we need to find the number of permutations of the chairs.

Let's break down the problem step by step:

Step 1: Find the total number of chairs.
The total number of chairs is 4 red + 3 yellow + 2 green = 9 chairs.

Step 2: Find the number of ways to arrange the chairs.
Since the chairs of the same color are indistinguishable, we can treat each color as a single unit. So, we have 3 units - 1 unit for red chairs, 1 unit for yellow chairs, and 1 unit for green chairs.

The number of ways to arrange these units is given by the formula n!/(n1! * n2! * n3! * ...), where n is the total number of units and n1, n2, n3, ... are the number of units of each type.

In our case, we have 9 units - 1 red unit, 1 yellow unit, and 1 green unit. So, the number of ways to arrange these units is 9!/(1! * 1! * 1!) = 9!.

Step 3: Simplify the expression.
9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 362,880.

Therefore, the number of ways to arrange the chairs is 362,880.

Step 4: Find the answer in the given options.
The correct answer is option 'B' - 1260.

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