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  • A game has the rule to shoot 19 balloons in total from the displayed red balloons, blue balloons, yellow balloons, green balloons and white balloons to get the reward. What is the number

A game has the rule to shoot 19 balloons in total from the displayed red balloons, blue balloons, yellow balloons, green balloons and white balloons to get the reward. What is the number of ways of shooting to get the reward?

Option: 1

\frac{23!}{4!19!}


Option: 2

\frac{32!}{4!19!}


Option: 3

19^{5}


Option: 4

Cannot be determined


Answers (1)

best_answer

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 identical varieties of balloons is =1+1+1+1+1=5

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=19+5-1=23}.

  • The number with which the restricted combination is to be made is \mathrm{=r-1=5-1=4}

Therefore, the required restricted combination is

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

=\mathrm{^{23}C_{r-1}}

=\frac{23!}{4!19!}

 

Posted by

shivangi.bhatnagar

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