Question
Download Solution PDFIf nC5 = nC7, then nC4 =
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
If \(\rm ^nC_x={^nC_y}\) then x + y = n
\(\rm ^nC_r=\frac{n\times(n-1)\times....(n-r+1)}{r!}\)
Calculation:
Given: nC5 = nC7
It is possible only when n = 5 + 7 = 12
∴ \(\rm ^nC_4=^{12}C_4=\frac{12\times11\times10\times9}{4!}\)
\(=\frac{12\times11\times10\times9}{4\times3\times2}\)
= 495
Hence, option (3) is correct.
Last updated on May 31, 2025
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