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  • There are many pencils, many erasers, many sharpeners, many sketch pens and many dot pens to choose from upon winning a lottery ticket. What is the number of ways of selecting 18 items in

There are many pencils, many erasers, many sharpeners, many sketch pens and many dot pens to choose from upon winning a lottery ticket. What is the number of ways of selecting 18 items in total from them?

Option: 1

7315


Option: 2

7153


Option: 3

18^{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 varieties of identical items 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=18+5-1=22}.

  • 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{=^{22}C_{4}}

=\frac{22!}{4!18!}

=7315

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