SOLUTION: Six students are lining up for flag ceremony. If three persons insist on standing next to each other, how many ways can the six students arrange themselves?
Question 1108562: Six students are lining up for flag ceremony. If three persons insist on standing next to each other, how many ways can the six students arrange themselves? Found 2 solutions by josmiceli, Edwin McCravy:Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website! The 3 that must be together can arrange
themselves 6 different ways:
a b c
a c b
b a c
b c a
c a b
c b a
P( 3,1 ) = 3! / 1!
P( 3,1 ) = 6
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Each one of these 6 possible groupings can
fit into the arrangements of the other 3 students:
( think of the 3 that must be together as one
student that 6 different identities )
144 different ways
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Definitely get a 2nd opinion if needed
The trio that must stand together can be arranged in 3! = 6 ways.
Then for each of those 6 ways, we have 4 "things" to arrange.
[The 4 "things" consist of 3 single persons and 1 trio.]
That's 4! - 24 ways.
Answer: 3!∙4! = 6∙24 = 144
Edwin