|Jul30-12, 11:08 AM||#18|
A problem concerning counting
|Jul30-12, 11:01 PM||#19|
wow..thanks a lot for providing such satisfying answers
|Jul31-12, 06:11 PM||#20|
Think of a box as containing four locations for books, and between them, and at the ends of the box, slots for very thin dividers, 5 slots in all. There are 14 dividers to go in each box and any number of them can occupy the same slot. When packing the box, left to right, a divider tells you to switch to the next book type. So the placement of dividers tells you exactly how a box is to be packed, and conversely, for any given choice of books for a box, arranging them in a canonical order determines the appropriate way to place the dividers; so this is a one-to-one mapping.
Now consider the book locations and dividers as just 18 things in a row. Four are book locations, 14 are dividers. Number of possible arrangements is 18 choose 4 = 3060.
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