Six students are equally divided into 3 groups, then, the three groups were assigned to three different topics. How many different arrangements W are possible?
Choose the correct choice from the following choices:	A) 30	B) 60	C) 90	D) 180	E) 540
90 is the number of ways you can assign 3 teams formed out of 12 people to 3 different tasks.   But now you can order the 3 tasks in 3! ways. T1 T2 T3 or T2 T1 T3.... etc etc.   I was confused between 90 and 540 but since question used the wordarrangementsdecided to go with complete arrangements W including the order of tasks.   could you explain the highlighted step... i'm getting 90 = 15 * 3!   suppose the students are numbered 1,2,3,4,5,6 and tasks are X,Y and Z   one of the 15 possible ways of forming teams is 12, 34, 56. these teams can be assigned to 3 tasks in 3! = 6 ways   X--	Y--	Z   12--	34--	56   12--	56--	34   34--	12--	56   34--	56--	12   56--	12--	34   56--	34--	12   so the answer should be 15*6= 
<gadget id="calculator">15*6</gadget>
<output>90</output>
90   But now you can fruther decide which task you want to perform first X Y or Z..=90
<result>C</result>
Six students are equally divided into 3 groups, then, the three groups were assigned to three different topics. How many different arrangements W are possible?