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The names of 18 students of class 12 and 20 students of class 11 are selected to form a quiz team of 15 students. But 9 among them cannot join as they already left for the excursion. 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!}{7!24!}


Option: 4

\frac{29!}{6!23!}


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 9 students 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=\left ( 18+20 \right )-9=29}.

  • The number with which the restricted combination is to be made is \mathrm{=r-k=15-9=6}

Therefore, the required restricted combination is

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

\mathrm{=^{29}C_{6}}

=\frac{29!}{6!23!}

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Gunjita

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