Answer: 1. 286 different combinations of players are possible.
2. The probability of selecting a team of 5 girls and 5 boys is [tex]\frac{63}{143}[/tex] and the decimal is 0.4405...
Step-by-step explanation:
1. Number of girls is 6 and number of boys is 7.
So, the total number of players = 6+7 = 13
A team of 10 players is to be selected from the class.
So, the total possible number of different combinations of players will be: [tex]^1^3C_{10} = \frac{13!}{10! (13-10)!}=\frac{13*12*11*10!}{10!*3!}= \frac{13*12*11}{6}=286[/tex]
2. Number of girls is 6 and number of boys is 7.
The possible number of teams by selecting 5 girls and 5 boys will be: [tex]^6C_{5}\times ^7C_{5} =6\times 21= 126[/tex]
and the number of total possible teams of 10 players [tex]= ^1^3C_{10} =286[/tex]
Thus, the probability of selecting a team of 5 girls and 5 boys [tex]=\frac{126}{286}= \frac{63}{143}[/tex] or [tex]0.4405...[/tex]
