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

Step-by-step solution

A committee of 11 members is to be formed form 8 males and 5 females. When atleast 6 males are included, the committee contains (6 Males and 5 females), (7 males and 4 females), (8 males and 3 Females) array ll & Required number of ways & = ^8 C ₆ ^5 C ₅+ ^8 C ₇ ^5 C ₄+ ^8 C ₈ ^5 C ₃ ~m =78 & When atleast 3 females are included, the & committee contains & (3 females and 8 males), (4 females and 7 males), & (5 females and 6 males) & Required number of ways & = ^5 C ₃ ^8 C ₈+ ^5 C ₄ ^8 C ₇+ ^5 C ₅ ^8 C ₆ & =78 & n =7