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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).

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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

THANKS FOR ALL HELP

Mar 3, 2019

#1
+111326
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Here's my best attempt...

a)

Possible sums of 10 =

2  3  5

2  4  4

2  6  2

3  3  4        4 possibilities

For each of these  there are   3 possible colors for the first card, 2 for the second and 1 for the third = 3 * 2 * 1 =

6 possibilities

So.....

4 possbilities * 6 possibilities = 24 ways

b)

Possible sums of 20

9 9 2        8  8  4         7  7  6

9 8 3        8  7  5

9 7 4        8  6  6

9 6 5

So   again....we have 8 possibilities * 6 possibilities =    48  ways

Mar 3, 2019
#2
+85
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I think that the order matters too, so wouldn't there be more?

alskdj  Mar 3, 2019
#3
+111326
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Order shouldn't matter

For instance....in the first part

2 blue, 3 red  and 5 green  is the same as

3 red , 2 blue and 5 green,  is the same as

5 green, 3 red, 2 blue....etc,

CPhill  Mar 3, 2019
#4
+85
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Oh... ok, thanks!

alskdj  Mar 3, 2019