For a positive integer

MATHEMATICS · Subjective · CBSE · Mathematics · Binomial Theorem · Binomial Theorem

Problem

n\ge 4

, compare the two binomial coefficients

\displaystyle {n\choose 3}

and

\displaystyle {n\choose 4}

. (a) Obtain an inequality relating

\displaystyle {n\choose 3}

and

\displaystyle {n\choose 4}

in terms of

n

. (b) Hence determine all integer values of

n

for which

\displaystyle {n\choose 3}\ge {n\choose 4}

and all values for which

\displaystyle {n\choose 3}<{n\choose 4}

. Justify your answer.