JEE MAIN - Mathematics (2021 - 17th March Morning Shift - No. 13)
Team 'A' consists of 7 boys and n girls and Team 'B' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then n is equal to :
5
2
4
6
توضیح
Total matches between boys of both team = $${}^7{C_1} \times {}^4{C_1} = 28$$
Total matches between girls of both team = $${}^n{C_1}\,{}^6{C_1} = 6n$$
Now, 28 + 6n = 52
$$ \Rightarrow $$ n = 4
Total matches between girls of both team = $${}^n{C_1}\,{}^6{C_1} = 6n$$
Now, 28 + 6n = 52
$$ \Rightarrow $$ n = 4