Question

In how many different ways can Robert order 3 objects from a set of 8 objects?

A.
20

B.
56

C.
60

D.
336

Answer 1

To determine the number of ways Robert can order 3 objects from a set of 8 objects, we need to use the concept of permutations. The number of permutations of \( r \) objects chosen from \( n \) objects is given by the formula:

\[
P(n, r) = \frac{n!}{(n - r)!}
\]

In this case, \( n = 8 \) and \( r = 3 \). Therefore, we need to calculate \( P(8, 3) \):

\[
P(8, 3) = \frac{8!}{(8 - 3)!} = \frac{8!}{5!}
\]

Now, calculating \( 8! \):

\[
8! = 8 \times 7 \times 6 \times 5!
\]

Thus, the \( 5! \) cancels out:

\[
P(8, 3) = \frac{8 \times 7 \times 6 \times 5!}{5!} = 8 \times 7 \times 6
\]

Now performing the multiplication:

\[
8 \times 7 = 56
\]
\[
56 \times 6 = 336
\]

Therefore, \( P(8, 3) = 336 \).

So the total number of different ways Robert can order 3 objects from a set of 8 objects is:

\[
\boxed{336}
\]