in how many ways can 8 students be assigned to 2 groups if each group must have at least 3 students.

answer key says it's 126. can someone explain? since it said "assigned" i tried permutations but my answers reach thousands and nothing close to 126 :(

Question

in how many ways can 8 students be assigned to 2 groups if each group must have at least 3 students.

answer key says it's 126. can someone explain? since it said "assigned" i tried permutations but my answers reach thousands and nothing close to 126 :(

anonymous · Answer

help please? :( @Hero @jim_thompson5910 @dpaInc @UnkleRhaukus @dumbcow @campbell_st etc. etc.

dumbcow · Answer

yeah order doesn't matter here so use combinations
there are 2 cases

case 1:  One group has 5 while other has 3 students  --> 8 choose 3  ways = 56
case 2:  Both groups have 4 students -->  8 choose 4  ways = 70

56+70 = 126

anonymous · Answer

thank youuu!!! now i see my mistake!!