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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?

(b) In how many ways can she draw one card from each color so that the sum of all the cards is 20?

Note that the colors matter, so 234 is different from 234 if the digits are different colors

 Jul 30, 2019
 #1
avatar+5798 
+1

\(a) \text{ The partitions of 10 are }\\ (2,2,6), ~(2,3,5),~(2,4,4),~(3,3,4),\\ \text{ and all arrangements of these among the colors}\\ \text{there will be $\dbinom{3}{1}+3! + \dbinom{3}{1}+\dbinom{3}{1} = 15$ arrangements}\)

 

\(b) \text{ Is basically the same deal but now we find the partition of 20 rather than 10}\\ (2,9,9),~(3,8,9),~(4,7,9),~(4,8,8),~(5,6,9),~(5,7,8),~(6,6,8),~(6,7,7),~\text{and all arrangements by color}\\ \text{as before this will be}\\ 3 + 3! + 3! + 3 + 3!+3! +3+3= 36\)

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 Jul 31, 2019
 #2
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+1

Hi, I your answer is wrong sad  I was able to solve the problem and verify my solution. 

 

A: 24

 

B: 48

 Jul 31, 2019
 #3
avatar+5798 
+1

list them

 

I maintain that 15 and 36 are the correct answers.

Rom  Aug 2, 2019
 #4
avatar+103715 
+1

15 is the first answer just like Rom says.

 

 

I also got 36 for the second one. 

Melody  Aug 2, 2019

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