Question

A committee of 11 members is to be formed from 8 males and 5 females. Let m denotes the number of ways of selecting committee having atleast 6 males and n denotes the number of ways of selecting atleast 3 females then

• A. m = n - 8
• B. m = n = 68
• C. m = n = 78
• D. m = n = 65

Answer 1

The Correct Option is C

Given that: (\(8\) males, \(5\) females)
Committee to be selected = \(11\) members
\(m\) = no. of ways the committee is formed with at least 6 males.
\((6M, 5F)\) or \((7M, 4F)\) or \((8M, 3F) \)
\(= ^8C_6 × ^5C_5+ ^8C_7 × ^5C_4+ ^8C_8 × ^5C_3\)
\(= 78 \)

\(n\) = no. of ways the committee is formed with atleast 3 female
\((8M, 3F)\) or \((7M, 4F)\) or \((6M, SF)\)
\(= ^8C_8 × ^5C_3 + ^8C_7 × ^5C_4 + ^8C_6 × ^5C_5 \)
\(= 10 + 40 + 28\)
\(= 78 \)
\(⇒ m = n = 78 \)

So, the correct option is (C): \(m = n = 78 \)