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Question
Find the value of 20C16 – 19C16
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Solution
20C16 – 19C16
= 19C16 + 19C15 – 19C16 ...[∵ nCr + nCr–1 = n+1Cr]
= 19C15
= `(19!)/(15!(19 - 15)!)`
= `(19!)/(15!4!)`
= `(19 xx 18 xx 17 xx 16 xx 15!)/(15! xx 4 xx 3 xx 2 xx 1)`
= 19 × 6 × 17 × 2
= 3876
∴ 20C16 – 19C16 = 19C15 = 3876
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