Question

How many different three-member teams can be formed from six students?(1 point)
Responses

20
20

120
120

216
216

720

Answers

GPT-4o mini
To find the number of different three-member teams that can be formed from six students, we can use the combination formula, which is given by:

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

where \( n \) is the total number of items to choose from (in this case, 6 students), \( r \) is the number of items to choose (in this case, 3 students), and \( ! \) denotes factorial.

Here, \( n = 6 \) and \( r = 3 \). Plugging these values into the formula, we get:

\[
\binom{6}{3} = \frac{6!}{3!(6-3)!} = \frac{6!}{3! \cdot 3!}
\]

Calculating the factorials:

- \( 6! = 720 \)
- \( 3! = 6 \)

Now, substitute these values into the equation:

\[
\binom{6}{3} = \frac{720}{6 \cdot 6} = \frac{720}{36} = 20
\]

Thus, the number of different three-member teams that can be formed from six students is **20**.