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denis23 [38]
4 years ago
10

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

Mathematics
1 answer:
Alenkasestr [34]4 years ago
7 0

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.

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