Question

Five red, two blue and 3 white balls are arranged in a row. If all the balls of the same colour are not distinguishable, how many different arrangements are possible

Answer 1

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Answer 2

The number of different arrangements possible, when arranged in a row if all the balls of the same color are not distinguishable, is 2520.

Given,

Red balls =  5

Blue balls = 2

White balls = 3

To Find,

Number of different arrangements possible when arranged in a row if all the balls of the same color are not distinguishable

Solution,

The total number of balls = 5 + 2 + 3

The total number of balls = 10

So, the total number of ways these can be arranged = 10!

But, it has been given that balls of the same color are indistinguishable,

Therefore, we need to divide 10! by the respective number of the same colored balls.

Red balls = 5

Blue balls = 2

White balls = 3

Final answer = $\frac{10!}{5! * 2! * 3!}$

Final answer = $\frac{10*9*8*7*6*5!}{5! * 2! * 3!}$

Final answer = $\frac{10*9*8*7*6}{2*1*3*2*1}$

Final answer = $\frac{30240}{12}$

Final answer = 2520

Hence, the number of different arrangements is 2520.

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