brents after - school game club has 12 members from which a six - member team is created. miguels after…
brents after - school game club has 12 members from which a six - member team is created. miguels after - school sports club has 10 members from which a six - member team is created. which students club has more possible combinations for his six - member team? o brents club has more possible team combinations because he has fewer members on each team than miguels does. o brents club has more possible team combinations because there are more members to choose from. o miguels club has more possible team combinations because there are fewer members in his club. o miguels club has more possible team combinations because he has more members on each team than brent does.
Answer
Explanation:
Step1: Recall combination formula
The combination formula is $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n$ is the total number of items and $r$ is the number of items to be chosen.
Step2: Calculate combinations for Brent's club
For Brent's club, $n = 12$ and $r=6$. So $C(12,6)=\frac{12!}{6!(12 - 6)!}=\frac{12!}{6!6!}=\frac{12\times11\times10\times9\times8\times7}{6\times5\times4\times3\times2\times1}=924$.
Step3: Calculate combinations for Miguel's club
For Miguel's club, $n = 10$ and $r = 6$. So $C(10,6)=C(10,4)$ (since $C(n,r)=C(n,n - r)$), and $C(10,4)=\frac{10!}{4!(10 - 4)!}=\frac{10!}{4!6!}=\frac{10\times9\times8\times7}{4\times3\times2\times1}=210$.
Step4: Compare the results
Since $924>210$, Brent's club has more possible combinations. This is because there are more members to choose from in Brent's club.
Answer:
Brent's club has more possible team combinations because there are more members to choose from.