Question

what is $_{9}c_{7}$?

choice

a. 66
b. 45
c. 55
d. 36

Explanation:

Step1: Recall the combination formula

The formula for combinations is \( _nC_r=\frac{n!}{r!(n - r)!} \), where \( n!=n\times(n - 1)\times\cdots\times1 \) and \( 0!=1 \). For \( _9C_7 \), we can also use the property \( _nC_r = _nC_{n - r} \), so \( _9C_7=_9C_{9 - 7}=_9C_2 \).

Step2: Calculate \( _9C_2 \)

Using the combination formula \( _nC_r=\frac{n!}{r!(n - r)!} \), substitute \( n = 9 \) and \( r = 2 \):

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Answer:

D. 36