MATHEMATICS MIDDLE SCHOOL

1. There are 6 girls and 7 boys in a class. A team of 10 players is to be selected from the class. How many different combinations of players are possible?2. There are 6 girls and 7 boys in a class. A team of 10 players is to be selected from the class. If the selection is random, what is the probability of selecting a team of 5 girls and 5 boys? what is the decimal?

Answers

Answer 1
Answer:

Answer:  1.  286 different combinations of players are possible.

2.  The probability of selecting a team of 5 girls and 5 boys is (63)/(143) 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:  ^1^3C_(10) = (13!)/(10! (13-10)!)=(13*12*11*10!)/(10!*3!)= (13*12*11)/(6)=286


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:  ^6C_(5)* ^7C_(5) =6* 21= 126

and the number of total possible teams of 10 players = ^1^3C_(10) =286

Thus, the probability of selecting a team of 5 girls and 5 boys =(126)/(286)= (63)/(143) or 0.4405...

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