Compund events

wowmaries:

How many different sums are possible for the numbers 4,2,3,7,3,4,6,5

Hi Wowmaries,
You have a time consuming question here!

2,3,3,4,4,5,6,7
3,3,4,4, pus 4 that are different

I am assuming that a 'sum' is referring to addition.
Add 2
3,3, 1 possibility
4,4, 1 posibility
both different 6C2
no of ways = 1+1+15 = 17

Add 3
3,3,plus another = 5
4,4 plus another = 5
all different = 6C3
no of ways = 5+5+20 = 30

Add 4
3,3,4,4, = 1
3,3, + 2diff = 5C2
4,4, + 2diff = 5C2
all diff = 6C4
no of ways = 1+10+10+15 = 36

Add 5
3,3,4,4, plus 1 diff = 4
3,3, plus 3diff = 5C3
4,4, plus 3 diff = 5C3
5 diff = 6C5
no of ways = 4+10+10+6 = 30

Add 6
3,3,4,4,plus 2 diff = 4C2
3,3,plus 4 diff = 5C4
4,4,plus 4 diff = 5C4
6 diff = 1
no of ways = 6+ 5+5+1 = 17

Add 7
3,3,4,4, plus 3 diff = 4C3
3,3,plus 5 dff = 1
4,4,plus 5 diff=1
no of ways = 4+1+1 = 6

Add 8
All of them =1

Grand total = 17+30+36+30+17+6+1 = 137
I may have made a stupid mistake but I think my technique is correct.