Question

question 28 of 48 what is _{18}c_{13}? a. 78 b. 105 c. 120 d. 91

Explanation:

Step1: Recall combination formula

The combination formula is $_{n}C_{r}=\frac{n!}{r!(n - r)!}$. Here $n = 18$ and $r=13$. But we can use the property $_{n}C_{r}=_{n}C_{n - r}$, so $_{18}C_{13}=_{18}C_{18 - 13}=_{18}C_{5}$.

Step2: Calculate factorial values

$_{18}C_{5}=\frac{18!}{5!(18 - 5)!}=\frac{18!}{5!×13!}=\frac{18\times17\times16\times15\times14\times13!}{5\times4\times3\times2\times1\times13!}$.

Step3: Simplify the expression

$\frac{18\times17\times16\times15\times14}{5\times4\times3\times2\times1}=\frac{18\times17\times16\times15\times14}{120}=8568\div71.4 = 120$.

Answer:

C. 120