Calculate the value of without evaluating the full factorial expressions

MATHEMATICS · Subjective · AoPS · Mathematics · Follow the Rules · Follow the Rules

Problem

Calculate the value of

^{20}C_{10}

without evaluating the full factorial expressions. (i) Write

^{20}C_{10}

in factorial form. (ii) Simplify the fraction step by step by cancelling common factors. (iii) State the final integer obtained.