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Question
Find the value of `""^20"C"_16 - ""^19"C"_16`
Sum
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Solution
`""^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
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Chapter 6: Permutations and Combinations - Exercise 6.6 [Page 89]
