Given:
[tex]_{11} \bsymbol{C}_{6}[/tex]
To find:
The value of the expression.
Solution:
Formula for [tex]_{n}{C}_{r}[/tex]:
[tex]$ _{n} C_{r}=\frac{n !}{r !(n-r) !} $[/tex]
Substitute n = 11 and r = 6.
[tex]$ _{11} C_{6}=\frac{11 !}{6 !(11-6) !} $[/tex]
[tex]$=\frac{11 !}{6 ! \cdot 5 !}$[/tex]
11! = 11 × 10 × 9 × ..... × 2 × 1 also can be written as 11 × 10 × 9 × 8 × 7 × 6!
[tex]$=\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6!}{6 ! \cdot 5 !}$[/tex]
Cancel the common factorials (6!).
[tex]$=\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7}{5 !}$[/tex]
5! = 5 × 4 × 3 × 2 × 1
[tex]$=\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7}{5 \cdot 4\cdot 3 \cdot 2 \cdot 1}$[/tex]
[tex]$=\frac{55440}{120}[/tex]
[tex]=462[/tex]
The value of the expression [tex]_{11} \bsymbol{C}_{6}[/tex] is 462.
