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Let us find the total number of matches that can be arranged between two teams where a boy plays against a boy and girl plays against a girl.

For Boys -

No of boys in team $1$$ = 6$

No of boys in team $2$ $ = 5$

We have to arrange single matches. This means that every boy from team $1$ will go against every boy of team $2$ .

Hence every boy from team $1$ will play $5$ matches i.e. $1$ match with every boy from team $2$

Since there are $6$ boys in team $1$

Therefore, total no of matches boys will play $6 \times 5 = 30$

For Girls –

No of girls in team $1 = 4$

No of girls in team $2 = 3$

As we did for boys same goes for girls i.e. every girl of team $1$ will compete with every girl of team $2$

Therefore, total no of matches girls will play$ = 4 \times 3 = 12$

Total no of matches $ = $ matches of boys $ + $ matches of girls

$ = 30 + 12 = 42$