select the correct answer.\nwhat is the number of possible combinations of 14 objects taken 3 at a time?\na…

Explanation:

Step1: Recall combination formula

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

Step2: Calculate factorials

First, find ( n!=14! = 14\times13\times12\times11\times\cdots\times1 ), ( k!=3! = 3\times2\times1=6 ), and ( (n - k)!=(14 - 3)!=11! = 11\times10\times\cdots\times1 ).

Step3: Substitute into formula

( C(14,3)=\frac{14!}{3!(14 - 3)!}=\frac{14\times13\times12\times11!}{6\times11!} ). The ( 11! ) terms cancel out.

Step4: Simplify the expression

( \frac{14\times13\times12}{6}=\frac{14\times13\times2}{1}=14\times26 = 364 ).

Answer:

A. 364