Question

Find the value of `""^20"C"_16 - ""^19"C"_16`

Answer 1

`""^20"C"_16 - ""^19"C"_16`

= `(20!)/(16!4!)-(19!)/(16!3!)`

= `(20xx19!)/(16!xx4xx3!)-(19!)/(16!3!)`

= `(19!)/(3!16!)[20/4-1]`

= `(19!)/(3!16!)(4)`

= `(19!)/(3!(16)(15!))4`

= `(19!)/(4(3!)(15!))`

= `(19!)/(4!15!)`

= ¹⁹C₁₅ or ¹⁹C₄ = 3876