Courtney buys 5 different shirts and 5 different sweaters. How many possible ways can she arrange them if the 5 shirts must hang together and the 5 sweaters on either or both sides?

Question

anonymous · Answer

i know the five shirts in the middle is 5! and on either side the sweaters can be arranged as 5! as well. but what about on both sides?

anonymous · Answer

@e.mccormick can you help?

anonymous · Answer

@surjithayer

e.mccormick · Answer

Well, if you think about it, what sorts of arrangments are you dealing with?  As in, what can change?  If you have shirts h1, h2, h3, h4, and h5 then sweaters w1, w2, w3, w4, and w5, then you could do:

h1, h2, h3, h4, h5,  w1, w2, w3, w4, w5
or
h2, h1, h3, h4, h5,  w1, w2, w3, w4, w5
or
w1, w2, w3, w4, w5, h1, h2, h3, h4, h5

and so on, right?

anonymous · Answer

yes including w1, w2, h1, h2, h3, h4, h5, w3, w4, w5 right?

e.mccormick · Answer

Yah.  So it is a large set of permutations.

Hmmm.  Basicaly, you have 5 items in some numer slots for the sweaters, and for each set of those, you have 5 items in 5 slots for the shirts.  Perhaps 5 in 10 for the sweaters.

anonymous · Answer

this isn't making sense

e.mccormick · Answer

Well, lets try a drawing.  If these are the sweaters in any order:
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