Nine pens are in the table.To create three pens in each group like as three group. How many ways are there to create these 3 teams? Choices
A) 27  B) 45  C) 90  D) 175  E) 280
Arrange the 6 pen in a straight line in 6! ways.   The first three form team 1, next three form team 2 and last three form team 3. But in each team, the boys are arranged in first, second third positions so you need to un-arrange them by dividing by 3! three times (once for each team). You get 6!/(2! * 2! * 2!)   Also, there are no distinct teams - team1, team2 and team3. You just have three teams. So you also need to un-arrange the three teams by dividing by another 3!.   You get 6!/(2! * 2! * 2!) * 2! = 45   Answer (45)   You get 6!/(2! * 2! * 2!) * 2!   Answer : 45
<result>B</result>
Nine pens are in the table.To create three pens in each group like as three group. How many ways are there to create these 3 teams?