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The names of 18 Geo-scientists and 20 Astro-physicists are selected to form a team of 10 scientists. But among them cannot join as they already left for the space mission.In how many ways can the team be made now?

Option: 1

\frac{31!}{7!2!}


Option: 2

\frac{10!}{7!24!}


Option: 3

\frac{31!}{3!28!}


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!\left ( y-x \right )!}}

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

Since 7 scientists must never be included in the team, the following is evident.

  • The number from which the restricted combination is to be made is \mathrm{=n-k=(18+20)-7=31}.

  • The number with which the restricted combination is to be made is

          \mathrm{=r-k=10-7=3}

Therefore, the required restricted combination is.

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

\mathrm{=^{31}C_{3}}

\mathrm{=\frac{31!}{3!28!}}

 

Posted by

vinayak

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