Given:
[tex]n=4[/tex] and [tex]r=3[/tex].
To find:
The combinations without repetition are possible if [tex]n=4[/tex] and [tex]r=3[/tex].
Solution:
Combination of selecting r item from total n items is:
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
We have [tex]n=4[/tex] and [tex]r=3[/tex]. By using the above formula, we get
[tex]^4C_3=\dfrac{4!}{3!(4-3)!}[/tex]
[tex]^4C_3=\dfrac{4\times 3!}{3!1!}[/tex]
[tex]^4C_3=4[/tex]
Therefore, the correct option is D.
