Question

perform the indicated calculation.
$\frac{_{7}c_{4}}{_{11}c_{4}}$
$\frac{_{7}c_{4}}{_{11}c_{4}}=square$ (round to the nearest thousandth as needed.)

Explanation:

Step1: Recall combination formula

The combination formula is $C(n,r)=\frac{n!}{r!(n - r)!}$. So, $_{7}C_{4}=\frac{7!}{4!(7 - 4)!}=\frac{7!}{4!3!}=\frac{7\times6\times5\times4!}{4!\times3\times2\times1}=35$.

Step2: Calculate $_{11}C_{4}$

Using the combination formula, $_{11}C_{4}=\frac{11!}{4!(11 - 4)!}=\frac{11!}{4!7!}=\frac{11\times10\times9\times8\times7!}{4!\times7!}=\frac{11\times10\times9\times8}{4\times3\times2\times1}=330$.

Step3: Calculate the ratio

$\frac{_{7}C_{4}}{_{11}C_{4}}=\frac{35}{330}\approx0.106$.

Answer:

$0.106$