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8 students are planning on splitting up into 3 (non-empty) study groups. How many ways can they split up into these study groups?

 

Note: It is possible that a study group contains only 1 person.

 Dec 17, 2019
 #1
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They can be split in:

 

[ 8 - 1] C [3 -1] =7 C 2 =21 ways

 Dec 17, 2019
 #2
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Thanks  answering Guest.

 

8 students are planning on splitting up into 3 (non-empty) study groups. How many ways can they split up into these study groups?

Note: It is possible that a study group contains only 1 person.

 

 

8 Students

 

If only the number of students in each group counts then

S*S*S*S*S*S*S*S       chose 3 stars from the 7   =  7C2  = 21 ways

(This is the same answer as guest got )

 

 

OR

 

If the exact students in each group is important then:

 

1,1,6        8C6               = 28

1,2,5         8C5*3           = 168

1,3,4         8C4*4           =  280

2,2,4         8C4*4C2      = 420

2,3,3         8C3*5C3      = 560

 

28+168+280+420+560 = 1456  ways

 

The first option looks right to me.  The second one I am much less sure about.

No guarentees for either.

 

Asker guest:  If you have a number answer can you please share it with the rest of us.

(If you believe it to be wrong please say why you think so.)

 Dec 17, 2019

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