Question

A local burger restaurant is having a contest to pick the restaurant’s 3 best-loved burgers out of 7 different burgers. How many ways are there to pick the top 3 burgers?(1 point)

Answer 1

To find the number of ways to choose the top 3 burgers from a total of 7 burgers, we can use the combination formula, which is expressed as:

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

Where:
- \( n \) is the total number of burgers,
- \( r \) is the number of burgers to choose,
- \( ! \) denotes factorial.

In this case, \( n = 7 \) and \( r = 3 \).

Now, we can calculate \( \binom{7}{3} \):

\[
\binom{7}{3} = \frac{7!}{3!(7-3)!} = \frac{7!}{3!4!}
\]

Calculating the factorials, we have:

- \( 7! = 7 \times 6 \times 5 \times 4! \)
- \( 3! = 3 \times 2 \times 1 = 6 \)
- \( 4! = 4 \times 3 \times 2 \times 1 = 24 \)

Thus, we can simplify \( \binom{7}{3} \) as follows:

\[
\binom{7}{3} = \frac{7 \times 6 \times 5 \times 4!}{3! \times 4!} = \frac{7 \times 6 \times 5}{3!} = \frac{7 \times 6 \times 5}{6} = 7 \times 5 = 35
\]

So, the number of ways to choose the top 3 burgers from 7 different burgers is:

\[
\boxed{35}
\]