Question

select the correct answer.
what is the number of possible combinations of 14 objects taken 3 at a time?
a. 364
b. 1,001
c. 2,184
d. 24,024

Explanation:

Step1: Recall combination formula

The formula for combinations is $$C(n,k)=\frac{n!}{k!(n-k)!}$$ where $n=14$, $k=3$.

Step2: Substitute values into formula

$$C(14,3)=\frac{14!}{3!(14-3)!}=\frac{14!}{3! \times 11!}$$

Step3: Simplify factorial expression

$$\frac{14 \times 13 \times 12 \times 11!}{3! \times 11!}=\frac{14 \times 13 \times 12}{3 \times 2 \times 1}$$

Step4: Calculate final value

$$\frac{2184}{6}=1001$$

Answer:

B. 1,001