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  • In how many ways can 5 identical red balls, 3 identical green balls, and 2 identical blue balls be arranged in a row?  Option: 1 55</p

In how many ways can 5 identical red balls, 3 identical green balls, and 2 identical blue balls be arranged in a row?

 

Option: 1

55


Option: 2

120


Option: 3

252


Option: 4

330


Answers (1)

best_answer

To solve this question, we need to calculate the number of permutations of the balls. We have 5 identical red balls, 3 identical green balls, and 2 identical blue balls.

The total number of balls is 5+3+2=10
The number of ways to arrange these balls is given by 10 ! ,which is equal to 3,628,800. However, since the red balls are identical (5 identical balls), the green balls are identical (3 identical balls), and the blue balls are identical (2 identical balls), we need to divide this result by the arrangements within each color.
To calculate the arrangements within each color, we divide by the factorials of the number of identical balls of each color 5 !, 3 ! \text {, and } 2 ! 
Therefore, the correct answer is \frac{10 !}{5 ! \times 3 ! \times 2 !}=\frac{3628800}{120 \times 6 \times 2}=252
Thus, the correct answer is 252.

 

 

 

Posted by

HARSH KANKARIA

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