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There are 2500 defective parts in the manufacturing unit. In how many ways can Kuldeep choose the 500 parts for melting in the shop such that 100 big-sized parts and 50 small–sized parts are already picked up?

Option: 1

\frac{2350!}{350!150!}


Option: 2

\frac{2350!}{350!2000!}


Option: 3

\frac{2500!}{350!2000!}


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 items from the different items with particular things always included is \mathrm{=^{n-k}C_{r-k}}

The number of parts already picked up is

=100+50

=150

Since 5 mathematics experts must always be included in the Quality Analyst, the following is evident.

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

         \mathrm{=n-k=2500-150=2350}.

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

         \mathrm{=r-k=500-150=350}

Therefore, the required restricted combination is

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

\mathrm{=^{2350}C_{350}}

=\frac{2350!}{350!2000!}

Posted by

Sanket Gandhi

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