Suggested languages for you:

Americas

Europe

Q20.

Expert-verifiedFound in: Page 641

Book edition
Middle English Edition

Author(s)
Carter

Pages
804 pages

ISBN
9780079039903

**Evaluate each expression.**

** **

**$C\left(12,4\right)\xb7C\left(8,3\right)$**

The value of $C\left(12,4\right)\xb7C\left(8,3\right)=27720$.

Given to evaluate the expression $C\left(12,4\right)\xb7C\left(8,3\right)$.

When *n* objects are available and *r* are to be picked then the number of combinations is given by $C\left(n,r\right)=\frac{n!}{\left(n-r\right)!r!}$

Using the formula:

$\begin{array}{l}C\left(12,4\right)\cdot C\left(8,3\right)=\frac{12!}{\left(12-4\right)!4!}\cdot \frac{8!}{\left(8-3\right)!3!}\\ C\left(12,4\right)\cdot C\left(8,3\right)=\frac{12!}{8!4!}\cdot \frac{8!}{5!3!}\\ C\left(12,4\right)\cdot C\left(8,3\right)=\frac{12\cdot 11\cdot 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5!}{8!\cdot 4\cdot 3\cdot 2\cdot 1}\cdot \frac{8!}{5!\cdot 3\cdot 2\cdot 1}\\ C\left(12,4\right)\cdot C\left(8,3\right)=27720\end{array}$

Hence, the value of $C\left(12,4\right)\cdot C\left(8,3\right)=27720$.

94% of StudySmarter users get better grades.

Sign up for free