Seperate the 12 face cards from a standard deck ofcards. Shuffle them. #1 - How

Question

Seperate the 12 face cards from a standard deck ofcards. Shuffle them. #1 - How many different arrangements can be made by selecting1 of each face card (i.e., jack, queen, king) from the pile? Combination or permutation? #2 - How many ways are there of selecting the queen of clubs,then the king of diamonds, and then the jack of hearts from thepile? Combination or permutation? Seperate the 12 face cards from a standard deck ofcards. Shuffle them. #1 - How many different arrangements can be made by selecting1 of each face card (i.e., jack, queen, king) from the pile? Combination or permutation? #2 - How many ways are there of selecting the queen of clubs,then the king of diamonds, and then the jack of hearts from thepile? Combination or permutation?

Explanation / Answer

When we're counting arrangements, order matters, hence this isa permutation: (1) jack and 1 queen and 1 king = P(4,1)*P(4,1)*P(4,1) = 64
Here we do not care about the order of each subgroup becausewe are picking from one card each time:
(2) Q of clubs then K of diamonds then J of hearts = C(1,1)*C(1,1)*C(1,1) = 1 Here we do not care about the order of each subgroup becausewe are picking from one card each time:
(2) Q of clubs then K of diamonds then J of hearts = C(1,1)*C(1,1)*C(1,1) = 1

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