From 4 gentleman and 4 ladies a committee of 5 is to be formed which consist of a president,vice-president and three secretaries.What will be the number of ways of selecting the commitee with atleast 3 women such that atleast one woman hols the post of president or vice-president?

1) 420
2) 610
3) 256
4) 512

• 3W, 2M
  Possibility that at least one W is P or VP = {Total possibility} - {possibility that both P and VP are men}
  
  4W, 1M
  In all cases at least one W holds the position of P or VP.
  
  3W, 2M + 4W, 1M
  [4C3*4C2*5!/3!]-[4C2*2*4C3] + 4C4*4C1*5!/3!
  432 + 80
  = 512
• 9 years agoHelpfull: Yes(2) No(0)
• ans is 512
• 9 years agoHelpfull: Yes(0) No(1)