Posted by -Z on Thursday, April 15, 2010 at 9:17pm.
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
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.
The answer is 56