Question

Can anyone help me understand this!!!! please break it down for me to understand!!

Answer 1

Given:

$_{11} \bsymbol{C}_{6}$

To find:

The value of the expression.

Solution:

Formula for $_{n}{C}_{r}$:

$_{n} C_{r}=\frac{n !}{r !(n-r) !}$

Substitute n = 11 and r = 6.

$_{11} C_{6}=\frac{11 !}{6 !(11-6) !}$

       $=\frac{11 !}{6 ! \cdot 5 !}$

11! = 11 × 10 × 9 × ..... × 2 × 1 also can be written as 11 × 10 × 9 × 8 × 7 × 6!

      $=\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6!}{6 ! \cdot 5 !}$

Cancel the common factorials (6!).

      $=\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7}{5 !}$

5! = 5 × 4 × 3 × 2 × 1

      $=\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7}{5 \cdot 4\cdot 3 \cdot 2 \cdot 1}$

      $=\frac{55440}{120}$

      $=462$

The value of the expression $_{11} \bsymbol{C}_{6}$ is 462.