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A shopkeeper displays several red kites, several blue kites, several green kites and several multicolour kites. What is the number of ways of selecting 16 kites in total from them?

Option: 1

969


Option: 2

329


Option: 3

16^{4}


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 kites is=1+1+1+1=4

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=16+4-1=19} .

  • The number from which the restricted combination is to be made is \mathrm{=r-1=4-1=3}.

Therefore, the required restricted combination is

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

=\mathrm{^{19}C_{3}}

=\frac{19!}{3!16!}

=969

 

 

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Rishi

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