Verified Solution • 2025–26 Session moderate

QJEEM19Ma7c08: JEE Main 2019 Mathematics - Class 11 JEEM19Ma7c08 Solution: A committee of 11 members is to be formed from 8 males and 5…

A committee of 11 members is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then :

Multiple Choice Options

  • A n = m – 8
  • B m = n = 78
  • C m + n = 68
  • D m = n = 68

Step-by-Step Verified Solution

At least 6 males means in the committee there can be 6 males or 7 males or 8 males.

∴\therefore m = 8C6×5C5+8C7×5C4+8C8×5C3{}^8{C_6} \times {}^5{C_5} + {}^8{C_7} \times {}^5{C_4} + {}^8{C_8} \times {}^5{C_3} = 78

At least 3 females means in the committee there can be 3 females or 4 females or 5 females.

∴\therefore n = 5C3×8C8+5C4×8C7+5C5×8C6{}^5{C_3} \times {}^8{C_8} + {}^5{C_4} \times {}^8{C_7} + {}^5{C_5} \times {}^8{C_6} = 78

So, m = n = 78

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