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  • 10 male and 12 female basketball players will be chosen to form a team of seven players. How many different ways are used to choose the team so that there are a maximum of two female play

10 male and 12 female basketball players will be chosen to form a team of seven players. How many different ways are used to choose the team so that there are a maximum of two female players on it?

 

Option: 1

18272


Option: 2

16372


Option: 3

19272

 


Option: 4

15472


Answers (1)

best_answer

Given that,

We have to form a team of 7 players from 10 male and 12 female basketball players.

Case I: Two female players are there on the team 

The number of ways to select the team is ^{10}C_{5} \times ^{_{12}}C_{2}

\begin{aligned} &{ }^{10} C_5 \times{ }^{12} C_2=\frac{10 !}{5 ! 5 !} \times \frac{12 !}{2 ! 10 !}\\ &{ }^{10} C_5 \times{ }^{12} C_2=16632 \end{aligned}

Case II: Only one female player is there in the team

The number of ways to select the team is    ^{10}C_{6} \times ^{_{12}}C_{1}

\begin{aligned} &{ }^{10} C_6 \times{ }^{12} C_1=\frac{10 !}{6 ! 4 !} \times \frac{12 !}{1 ! 11 !}\\ &{ }^{10} C_6 \times{ }^{12} C_1=2520 \end{aligned}

Case III: No female players are there on the team

The number of ways to select the team is ^{10}C_{7} \times ^{_{12}}C_{0}

\begin{aligned} &{ }^{10} C_7 \times{ }^{12} C_0=\frac{10 !}{7 ! 3 !} \end{aligned}

\begin{aligned} &{ }^{10} C_7 \times{ }^{12} C_0=120 \end{aligned}

Therefore, the total number of ways is 16632+2520+120 = 19272

 

 

Posted by

seema garhwal

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