Posted by Z on .
Diane has one stamp of each positive integer value 1 cent through 9 cents, inclusive. She wants to put 10 cents worth of postage in a row across the top of an envelope. If arrangements of the same stamps in different order are considered different, how many arrangements are possible?

Math 
Reiny,
Make a list of combinations.
2 stamps: 1,9
number of ways to arrange = 2
3 stamps: 1,2,7  1,3,6  1,4,5  2,3,5
number of ways to arrange = 4(3!) = 24
4 stamps: 1,2,3,4  that is all of them
number of ways to arrange = 1(4!) = 24
total number of ways = 2+24+24 = 50 
Math 
Alex,
Try doing it with casework.
Case: 1
1,9 x2
2,8 x2
3,7 x2
4,6 x2
2+2+2+2=8.
That's it for case one since Diane only has one stamp for each.
Case: 2
1,2,7 x6
1,3,6 x6
1,4,5 x6
2,3,5 x6
6+6+6+6=24.
Case: 3
1,2,3,4 x24
The total answer is 8+24+24=56. 
Math 
Robert,
The answer is 56