Answer:
226 teams
Step-by-step explanation:
A team can be:
Count all combinations:
1. 5 girls from 5 girls can be chosen in 1 way.
2. 4 girls from 5 girls can be chosen in
[tex]C^5_4=\dfrac{5!}{4!(5-4)!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 3\cdot 4\cdot 1}=5[/tex]
different ways and 1 boy from 5 boys can be chosen in
[tex]C^5_1=\dfrac{5!}{1!(5-1)!}=\dfrac{5!}{1!\cdot 4!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 3\cdot 4\cdot 1}=5[/tex]
different ways, so in total,
[tex]5\cdot 5=25[/tex]
different combinations.
3. 3 girls from 5 girls can be chosen in
[tex]C^5_3=\dfrac{5!}{3!(5-3)!}=\dfrac{5!}{3!\cdot 2!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 3\cdot 1\cdot 2}=10[/tex]
different ways and 2 boys from 5 boys can be chosen in
[tex]C^5_2=\dfrac{5!}{2!(5-2)!}=\dfrac{5!}{2!\cdot 3!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 1\cdot 2\cdot 3}=10[/tex]
different ways, so in total,
[tex]10\cdot 10=100[/tex]
different combinations.
4. 2 girls from 5 girls can be chosen in
[tex]C^5_2=\dfrac{5!}{2!(5-2)!}=\dfrac{5!}{2!\cdot 3!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 1\cdot 2\cdot 3}=10[/tex]
different ways and 3 boys from 5 boys can be chosen in
[tex]C^5_3=\dfrac{5!}{3!(5-3)!}=\dfrac{5!}{3!\cdot 2!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 3\cdot 1\cdot 2}=10[/tex]
different ways, so in total,
[tex]10\cdot 10=100[/tex]
different combinations.
In total, there are
[tex]1+25+100+100=226[/tex]
possible teams.
