Solve the given commutation\[^{{\text{11}}}{{\text{C}}_{\text{8}}}\]?

Hint:For commutation you have to know that this process is a kind of selection process from the terms given for a particular set, with the help of this identity you can find a certain number of possibilities that can happen from the given set for a particular task.

The general formulae of commutation are:
\[{ \Rightarrow ^n}{C_m} = \dfrac{{n!}}{{\left( {n - m} \right)!}}\]

Here the “!” sign represents a factorial value for the given value.

Formulae Used:
 \[^n{C_m} = \dfrac{{n!}}{{\left( {n - m} \right)!}}\]

Complete step by step solution:
For the given value \[^{{\text{11}}}{{\text{C}}_{\text{8}}}\]

We can use the formulae of commutation and then obtain the value accordingly, by implying the formulae we have to elaborate the factorial terms and then the fraction obtained needs some simplification which can give you the least possible fraction, on solving we get:

\[{ \Rightarrow ^{{\text{11}}}}{{\text{C}}_{\text{8}}} = \dfrac{{11!}}{{\left( {11 - 8} \right)!}} =
\dfrac{{11!}}{{3!}} = \dfrac{{11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times
3 \times 2 \times 1}}{{3 \times 2 \times 1}} = 6652800\]

Here on doing factorial we got the same numbers in numerator and denominator which get cancelled out and finally the smallest possible fraction is obtained whose denominator is one which is not written in general.

Additional Information: Permutation and combination needs factorial to be solved, factorial of any number can be given as multiply the numbers and then by every small integer from that integer up to one, the product will give you the factorial of that number.

Note: Permutation and commutation is a selection process from the given set of solutions, once you need to find the number of possibilities for a statement or task you can arrange the possibilities and then with the help of permutation and combination you can see how many possible outcomes are there.