Mathematics

Problem

For the integer

n=18

consider the pair of binomial coefficients

{^{18}C_5}

and

{^{18}C_{13}}

. (a) Compute

{^{18}C_5}

using factorials. (b) Obtain

{^{18}C_{13}}

without any new factorial expansion. (c) Find the product

{^{18}C_5}\times {^{18}C_{13}}

and express your answer as a single quotient of factorials in its simplest form.