Question

List all the combinations of 4 objects 1, 2, 3, and 4 taken 3 at a time. What is $C(4,3)$?

Short answer

The list of combinations is 123, 124, 134, 234.

The value of the given combination is 4.

Step-by-step solution

Step 1. Given information.

3 objects are taken at a time from 4 objects 1, 2, 3, and 4 at a time.

The given combinations is $C(4,3)$.

Step 2. Determine the list of combinations.

The list of combinations is:

123, 124, 134, 234

Step 3. Determine the value of combination.

We know that,

$C(n,r)=\frac{n!}{(n-r)!r!}$

Using the above formula, we get

$\begin{array}{rcl}C(4,3)& =& \frac{4!}{(4-3)!3!}\\ & =& \frac{4!}{1!3!}\\ & =& \frac{4\times 3!}{1\times 3!}\\ & =& 4\end{array}$