Question
How many different three-member teams can be formed from six students?(1 point)
Responses
20
20
120
120
216
216
720
Responses
20
20
120
120
216
216
720
Answers
There are no human answers yet.
Answered by
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**.
\[
\binom{n}{r} = \frac{n!}{r!(n-r)!}
\]
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**.
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