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Fish181
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The symbol \( \binom{n}{r}\) is defined for positive integers n and r, where n > r, by the equation \( \binom{n}{r}= \frac{n!}{r!(n-r)!}\). Which of the following equals \( \binom{17}{6}\)?
A. \(\frac{17}{6} \binom{16}{5}\)
B. \(17 \binom{16}{6}\)
C. \(\binom{18}{5}\)
D. \(\binom{23}{17}\)
E. \(\binom{16}{5}\)
GMAT-Club-Forum-hwz00g85.png [ 7.88 KiB | Viewed 4038 times ]
GMAT-Club-Forum-oo663cjv.png [ 3.82 KiB | Viewed 4051 times ]
A. \(\frac{17}{6} \binom{16}{5}\)
B. \(17 \binom{16}{6}\)
C. \(\binom{18}{5}\)
D. \(\binom{23}{17}\)
E. \(\binom{16}{5}\)
\( \binom{n}{r}\)
Attachment:
GMAT-Club-Forum-hwz00g85.png [ 7.88 KiB | Viewed 4038 times ]
Attachment:
GMAT-Club-Forum-oo663cjv.png [ 3.82 KiB | Viewed 4051 times ]
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26 May 2024, 12:54
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Fish181
\( \binom{17}{6} = \)
\(=\frac{ 17!}{6!(17-6)!}= \)
\(=\frac{ 17!}{6!11!}= \)
\(=\frac{ 17*16!}{(6*5!)11!}= \)
\(=\frac{17}{6}*\frac{ 16!}{5!11!}= \)
\(= \frac{17}{6} \binom{16}{5}\)
Attachment:
GMAT-Club-Forum-rcw9kcxe.png [ 7.88 KiB | Viewed 4041 times ]
Attachment:
GMAT-Club-Forum-7dns5ksu.png [ 3.82 KiB | Viewed 4034 times ]
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