IPMAT Rohtak 2020 (QA) - Please calculate in how many ways can a platoon of sixteen soldiers be chosen out of a total of twenty soldiers for a surgical strike? | PYQs + Solutions

IPMAT Rohtak 2020

Modern Math

Permutation & Combination

Conceptual

Please calculate in how many ways can a platoon of sixteen soldiers be chosen out of a total of twenty soldiers for a surgical strike?

4845

4800

4855

4955

Correct Option: 1

This is a straightforward combination problem where we need to select 16 soldiers from 20 soldiers.

Using the combination formula:

^{20}C_{16}

\frac{20!}{16!(20-16)!}

\frac{20!}{16!4!}

= \frac{20 × 19 × 18 × 17 × 16!}{16! × 4 × 3 × 2 × 1}

= \frac{20 × 19 × 18 × 17}{4 × 3 × 2 × 1}

= \frac{116280}{24}

= 4845

Therefore, 4845 different platoons can be chosen.

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