For us to be able to determine the possible combinations of 4 number from the list of 5 numbers (12, 13, 14, 15, 16), we will be using the following formula:
[tex]\text{ C(n,k) = }\frac{n!}{k!(n\text{ - k)!}}[/tex]Where,
n = total numbers of sample in the list = 5
k = selected numbers in the list = 4
We get,
[tex]\text{ C(n,k) = }\frac{n!}{k!(n\text{ - k)!}}[/tex][tex]\text{ C(5,4) = }\frac{5!}{4!(5\text{ - 4)!}}[/tex][tex]\text{= }\frac{5!}{4!\cdot1\text{!}}[/tex][tex]\text{= }\frac{(5\text{ x 4 x 3 x 2 x 1)}}{\text{ (4 x 3 x 2 x 1)(1)}}[/tex][tex]\text{ = }\frac{120}{24\text{ x 1}}\text{ = }\frac{120}{24}[/tex][tex]\text{ C(5,4) = 5}[/tex]Therefore, the answer is letter B.
