Question
How many possible committees of two people can be formed from a group of six people
Answers
GPT-4o mini
To find the number of possible committees of two people that can be formed from a group of six people, 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 people, \( r \) is the number of people to choose, and \( ! \) denotes factorial.
In this case, we have \( n = 6 \) and \( r = 2 \). Plugging in the values, we get:
\[
\binom{6}{2} = \frac{6!}{2!(6-2)!} = \frac{6!}{2! \times 4!}
\]
Now calculate the factorials:
- \( 6! = 6 \times 5 \times 4! \)
- \( 2! = 2 \times 1 = 2 \)
- \( 4! = 4 \times 3 \times 2 \times 1 = 24 \)
Substituting these into the equation, we get:
\[
\binom{6}{2} = \frac{6 \times 5 \times 4!}{2! \times 4!} = \frac{6 \times 5}{2} = \frac{30}{2} = 15
\]
Thus, the number of possible committees of two people that can be formed from a group of six people is \( \boxed{15} \).
\[
\binom{n}{r} = \frac{n!}{r!(n-r)!}
\]
where \( n \) is the total number of people, \( r \) is the number of people to choose, and \( ! \) denotes factorial.
In this case, we have \( n = 6 \) and \( r = 2 \). Plugging in the values, we get:
\[
\binom{6}{2} = \frac{6!}{2!(6-2)!} = \frac{6!}{2! \times 4!}
\]
Now calculate the factorials:
- \( 6! = 6 \times 5 \times 4! \)
- \( 2! = 2 \times 1 = 2 \)
- \( 4! = 4 \times 3 \times 2 \times 1 = 24 \)
Substituting these into the equation, we get:
\[
\binom{6}{2} = \frac{6 \times 5 \times 4!}{2! \times 4!} = \frac{6 \times 5}{2} = \frac{30}{2} = 15
\]
Thus, the number of possible committees of two people that can be formed from a group of six people is \( \boxed{15} \).