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Find the number of ways of selecting 10 balls out o fan unlimitednumber of identical white, red, and blue balls.

Answer» Correct Answer - `.^(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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