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  • There are an unlimited number of identical balls of red colour, unlimited number of identical balls of blue colour, and unlimited number of identical balls of green colour. What is the nu

There are an unlimited number of identical balls of red colour, unlimited number of identical balls of blue colour, and unlimited number of identical balls of green colour. What is the number of ways of selecting 12 balls in total from them?

Option: 1

91


Option: 2

19


Option: 3

12^{3}


Option: 4

Cannot be determined


Answers (1)

Note the following:

  • The formula for the combination for the selection of the \mathrm{x} items from the \mathrm{y}different items is \mathrm{=^{y}C_{x}=\frac{y!}{x!(y-x)!}}

  • The number of ways of allocating the \mathrm{n} identical items among \mathrm{r} head count with zero, one or more items is \mathrm{=^{n+r-1}C_{r-1}}

As per the available data, the number of colours is \mathrm{=1+1+1=3}

Note that the following is evident from the provided data.

  • The number from which the restricted combination is to be made is \mathrm{=n+r-1=12+3-1=14} .

  • The number with which the restricted combination is to be made is \mathrm{=r-1=3-1=2}

Therefore, the required restricted combination is

\mathrm{=^{n+r-1}C__{r-1}}

\mathrm{=^{14}C_{2}}

=\frac{14!}{2!12!}

=91

Posted by

Kshitij

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