Question

What is the value of ${}^4{C}_2$?

Answer 1

Step 1: Not the given data

Given expression is ${}^4{C}_2$

Combination: A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

The general formula for finding the combination of expressions is ${}^n{C}_r=\frac{n!}{r!(n-r)!}$

Step 2: Finding the required value of the given expression

Now

${}^4{C}_2=\frac{4!}{2!(4-2)!}$

$$\begin{gathered} =\frac{4\times 3\times 2\times 1}{2!\times 2!} \\ =\frac{4\times 3\times 2\times 1}{2\times 1\times 2\times 1}\left[\because n!=n\times (n-1)\times (n-2)\times ...\times 2\times 1\right] \\ =3\times 2 \\ =6 \end{gathered}$$

$\therefore {}^4{C}_2=6$

Hence, the correct option is $6$.