A group of 10 army persons is to be sent on a mission. The group is to be selected from six men commanders and ten lieutenants comprising of 5 men lieutenants and 5 women lieutenants. In how many ways can this be done, if the group must have at least four commanders and at least four lieutenants with at least 2 men lieutenants and 2 women lieutenants?

• 6 commanders, 5 women lieutenants, 5 men lieutenants.
  there will be at least 4 commanders, 2 female lieutenants, 2 male lieutenants.
  so the combinations will be = (6C4 * 5C3 * 5C3)+(6C4 * 5C2 * 5C4)+ (6C4 * 5C4 * 5C2)+ (6C5 * 5C3 * 5C2)+(6C5 * 5C2 * 5C3)+ (6C6 * 5C2 * 5C2)
  
  please calculate the ans on your own :D :P
• 9 years agoHelpfull: Yes(6) No(3)
• possible combination
  (6 commandr) (5 women) (5 men)
  4 3 3 => (6C4 * 5C3 * 5C3)
  4 2 4 => (6C4 * 5C2 * 5C4)
  4 4 2 => (6C4 * 5C4 * 5C2)
  5 3 2 => (6C5 * 5C3 * 5C2)
  5 2 3 => (6C5 * 5C2 * 5C3)
  6 2 2 => (6C6 * 5C2 * 5C2)
  
  Add all those, that wiil be answer
• 7 years agoHelpfull: Yes(0) No(0)
• 6Comm 5Women 5Men
  433= (6c4 * 5c3 * 5c3)= 15x10x10= 1500+
  424= (6c4 * 5c2 * 5c4)= 15x10x5 = 750+
  442= (6c4 * 5c4 * 5c2)= 15x10x5= 750+
  532= (6c5 * 5c3 * 5c2)= 6x10x10= 600+
  523= (6c5 * 5c2 * 5c3)= 6x10x10= 600+
  622= (6c6 * 5c2 * 5c2)= 1x10x10= 100
  ----------------------------
  Total = 4300
• 6 years agoHelpfull: Yes(0) No(0)