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  • Group A has 9 men and n women, while Group B has 6 men and 6 women. If these two teams can arrange a total of 66 single matches in which men play against men and women play against women,

Group A has 9 men and n women, while Group B has 6 men and 6 women. If these two teams can arrange a total of 66 single matches in which men play against men and women play against women, then the value of n equals to

 

Option: 1

4


Option: 2

2


Option: 3

6

 


Option: 4

8


Answers (1)

best_answer

Given that,

Group A has 9 men and n women, and Group B has 6 men and 6 women.

The total number of matches between the boys from Group A ad Group B is given by,

\begin{aligned} &{ }^9 C_1 \times{ }^6 C_1=9 \times 6\\\\ &{ }^9 C_1 \times{ }^6 C_1=54 \end{aligned}

The total number of matches between the girls from Group A and Group B is given by, 

{ }^n C_1 \times{ }^6 C_1=6 n

The two teams can arrange a total of 66 single matches.

Thus,

\begin{aligned} & 54+6 n=66 \\ & 6 n=12 \\ & n=2 \end{aligned}

Therefore, the value of n is 2.

 

Posted by

Nehul

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