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  • The school A nominates16 students, the school B nominates18 students and the school C nominates16 students to participate in a quiz team of 15 students. However, 9 among them are already

The school A nominates16 students, the school B nominates18 students and the school C nominates16 students to participate in a quiz team of 15 students. However, 9 among them are already confirmed while another 8 cannot join due to on-going scholarship exams. In how many ways can the team be made now?

Option: 1

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


Option: 2

\frac{55!}{18!17!}


Option: 3

\frac{35!}{19!17!}


Option: 4

\frac{33!}{6!27!}


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

Since 9 students must always be included in the quiz team and another 8 cannot join the team, the following is evident.

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

          \mathrm{=n-k-h=\left ( 16+18+16 \right )-9-8=33}.

  • 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-h}C_{r-k}}

\mathrm{=^{33}C_{6}}

\mathrm{=\frac{33!}{6!27!}}

Posted by

Rishabh

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