Counting math

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I have some questions about counting principles in mathematics:

If I had standard deck of 52 playing cards, then

a. How many ways can one draw a heart or a spade?
b. " " an ace or a king?
c. " " a card numbered 2 through 10?
d. " " a card numbered 2 through 10 or a king?

I got these answers (using the addition rule of a disjoint union and the multiplication rule):

a. Let A = cards that are hearts and B = cards that are spades.
|A| + |B| = 13 + 13 = 26
b. Let A = aces and B = kings
|A| + |B| = 4 + 4 = 8
c. Let A = {2, 3, 4, ... 10 belonging to hearts}, B = {2...10 belonging to spades}, C = {2...10 belonging to diamonds}, and D = {2...10 belonging to clubs}
|A| + |B| + |C| + |D| = 9 + 9 + 9 + 9 = 36
d. Take previous answer and add to 4 (Let E = kings):
36 + |E| = 40

Am I correct as far as using these rules? Thanks.
 
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  • #2
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I have some questions about counting principles in mathematics:

If I had standard deck of 52 playing cards, then

a. How many ways can one draw a heart or a spade?
b. " " an ace or a king?
c. " " a card numbered 2 through 10?
d. " " a card numbered 2 through 10 or a king?

I got these answers (using the addition rule of a disjoint union and the multiplication rule):

a. Let A = cards that are hearts and B = cards that are spades.
|A| + |B| = 13 + 13 = 26
b. Let A = aces and B = kings
|A| + |B| = 4 + 4 = 8
c. Let A = {2, 3, 4, ... 10 belonging to hearts}, B = {2...10 belonging to spades}, C = {2...10 belonging to diamonds}, and D = {2...10 belonging to clubs}
|A| + |B| + |C| + |D| = 9 + 9 + 9 + 9 = 36
d. Take previous answer and add to 4 (Let E = kings):
36 + |E| = 40

Am I correct as far as using these rules? Thanks.
Very late reply, but these all look correct to me.
 

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