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Find the number of ways of selecting 10 ...

Find the number of ways of selecting 10 balls out of fun unlimited number of identical white, red, and blue balls.

Text Solution

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The correct Answer is:
`.^(12)C_(2)`
Let `x_(W),x_(R ),x_(B)` be the number of white balls, red balls, and blue balls being selected. We must have
`x_(W)+x_(R )+x_(B)=10`
The required number of ways is equal to the number of non-negative integers solutions of `x_(W)+x_(R )+x_(B)=10`, which is `.(3+10-1)C_(10)= .^(12)C_(10)= .^(12)C_(2)`.
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