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JEE MATHEMATICS MCQ: COMBINATIONS

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If

\sum\limits_{r = 0}^{25} {\left\{ {{}^{50}{C_r} \cdot {}^{50 - r}{C_{25 - r}}} \right\} = K\left( {{}^{50}{C_{25}}} \right)}

. Then,

K

is equal to

View answer and explanation

Correct option: C

{2^{25}}

Option C (

{2^{25}}

) is correct because the given summation simplifies to

{2^{25}}

after applying combinatorial identities.

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n