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  • There are many B. Tech engineers, many diploma engineers, and many draftsmen applied for the written test. What is the number of ways of selecting 50 candidates in total from them?<di

There are many B. Tech engineers, many diploma engineers, and many draftsmen applied for the written test. What is the number of ways of selecting 50 candidates in total from them?

Option: 1

1326


Option: 2

1329


Option: 3

50^{3}


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 number of ways of allocating the \mathrm{n} identical items among \mathrm{r} head count with zero, one or more items is \mathrm{=^{n+r-1}C_{r-1}}

As per the available data, the number of identical professions is \mathrm{=1+1+1=3}

Note that the following is evident from the provided data.

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

          \mathrm{=n+r-1=50+3-1=50}

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

         \mathrm{=r-1=3-1=2}

Therefore, the required restricted combination is

\mathrm{=^{n+r-1}C_{r-1}}

\mathrm{=^{52}C_{2}}

=\frac{52!}{2!50!}

=1326

Posted by

Suraj Bhandari

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