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There are 2 identical white balls, 3 identical red balls and 4

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There are $2$ identical white balls, $3$ identical red balls and $4$ green balls of different shades. The number of ways in which they can be arranged in a row so that at least one ball is separated from the balls of the same color is

6 (7! - 4!)

7 (6! - 4!)

8! - 5!

n o n e

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There are

2

identical white balls,

3

identical red balls and

4

green balls of different shades. The number of ways in which they can be arranged in a row so that at least one ball is separated from the balls of the same color is

7 mins ago

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Text solutionVerified

Here it can be solved by the total cases minus the number of cases in which no ball is separated.

∵

green balls are of different shades

∴

total cases

= \frac{9 !}{2 ! 3 !}

Number of cases in all are together considering

2

white ball as

1

unit,

3

red ball as other and

4

green ball as

3 r d

3!

However, intra permutation among

4

green ball will take place,

∴

No. of ways

= \frac{9 !}{2 ! 3 !} - 3! \times 4!

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Question Text	There are $2$ identical white balls, $3$ identical red balls and $4$ green balls of different shades. The number of ways in which they can be arranged in a row so that at least one ball is separated from the balls of the same color is
Answer Type	Text solution:1
Upvotes	150

There are 2 identical white balls, 3 identical red balls and 4 green balls of different shades. The number of ways in which they can be arranged in a row so that at least one ball is separated from the balls of the same color is

Text solutionVerified

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There are $2$ identical white balls, $3$ identical red balls and $4$ green balls of different shades. The number of ways in which they can be arranged in a row so that at least one ball is separated from the balls of the same color is