I have been asked to discuss this question further.
I have only looked at part A again. I assume the problem with part A is the same as that of part B.
Lizzie has a strange deck of 24 number cards that contains cards labeled 2 through 9 in three different colors (red, blue, and green).
(a) In how many ways can she draw one card from each color so that the sum of all the cards is 10?
The only triads that add to 10 are
6,2,2
5,2,3
4,4,2
4,3,3
If you think there is a problem with this so far then let me know.
Consider 6,2,2
The 6 can be red blue or green 3 choices. Once the 6 is allocated a colour, both the other colours must be 2.
SO there are 3 ways to allocate 6,2 and 2 if each one must be a different colour.
The same logic can be used for 4,4,2 and for 4,3,3
So far there is 3+3+3=9 ways
The only triad not considered so far is 5,2,3
The 5 can be one of 3 colours, the 2 can be one of 2 remaining colours and the 3 must be the last colour. So that is 3*2=6 possibilities.
9+6 = 15 ways that this can be done.
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Think about it, see if you can get 36 for the second one by yourself.