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  • In how many ways can a collection of 25 fishes be made for a new aquarium from 16 Guppies, 13 Goldfishes, 11 Angel fishes and 15 barbs among whom 5 fishes are found dead and 12 healthy fi

In how many ways can a collection of 25 fishes be made for a new aquarium from 16 Guppies, 13 Goldfishes, 11 Angel fishes and 15 barbs among whom 5 fishes are found dead and 12 healthy fishes must always be included in the collection?

Option: 1

\frac{35!}{18!17!}


Option: 2

\frac{25!}{18!17!}


Option: 3

\frac{25!}{13!12}


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 combination for the selection of the \mathrm{r} items from the \mathrm{n} different items with \mathrm{k} particular things always included and particular things always excluded is \mathrm{=^{n-k-h}C_{r-k}}

Since 5 fishes are found dead and 12 healthy fishes must always be included in the collection, the following is evident. 16 Guppies, 13 Goldfishes, 11 Angel fishes and 15 barbs

  • The number from which the restricted combination is to be made is \mathrm{=n-k-h=(16+3+11+15)-12-5=38} .

  • The number with which the restricted combination is to be made is \mathrm{=r-k=25-12=13}

Therefore, the required restricted combination is

\mathrm{=^{n-k-h}C_{r-k}}

\mathrm{=^{25}C_{13}}

=\frac{25!}{13!12!}

Posted by

Irshad Anwar

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