# Arrangements question

Watch
Announcements
#1
Question:
I have fifteen books of three different sizes, five of each. In how many ways can I arrange them on my shelf if I keep books of the same size together?
My method
15 books
3 different sizes
five each size

lets say 5 books are large - L
5 books are medium - M
5 books are small - S

Position: L L L L L M M M M M S S S S S
number of Possibilities: 5 4 3 2 1 5 4 3 2 1 5 4 3 2 1

thus the number of ways = 5 x 4 x 3 x 2 x 1 x 5 x 4 x 3 x 2 x 1 x 5 x 4 x 3 x 2 x 1 = 1728000

but the answer given by the book is 10 368 000
Please can some one why the answer is 10 368 000 and where did i go wrong?

thank you
0
10 months ago
#2
That's good so far. You can have the clumps of sizes in different orders as well, it needn't be Larges, then Mediums, then Smalls.
1
X

new posts
Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### Poll

Join the discussion

Yes (68)
61.82%
No (42)
38.18%