Question

select the correct answer.
what is the number of possible combinations of 8 objects taken 6 at a time?
a. 20,160
b. 3,360
c. 2,520
d. 28

Explanation:

Step1: Recall combination formula

The formula for combinations is \( C(n, k)=\frac{n!}{k!(n - k)!} \), where \( n = 8 \) and \( k = 6 \).

Step2: Substitute values into formula

Substitute \( n = 8 \) and \( k = 6 \) into the formula: \( C(8, 6)=\frac{8!}{6!(8 - 6)!}=\frac{8!}{6!2!} \).

Step3: Simplify factorials

We know that \( n!=n\times(n - 1)\times\cdots\times1 \), so \( 8! = 8\times7\times6! \) and \( 2! = 2\times1 \). Substituting these in, we get \( \frac{8\times7\times6!}{6!\times2\times1} \).

Step4: Cancel and calculate

The \( 6! \) terms cancel out, leaving \( \frac{8\times7}{2\times1}=\frac{56}{2} = 28 \).

Answer:

D. 28