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In a pack of 42 cards, 3 cards are chosen one after the other. Find the number of ways this can be done…

Drawing cards one after another without replacement is an ordered selection, so the count is the permutation \(^{42}P_3=42\times41\times40=68880\). The first card can be any…

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In a pack of 42 cards, 3 cards are chosen one after the other. Find the number of ways this can be done without replacement:

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Correct answer C

Drawing cards one after another without replacement is an ordered selection, so the count is the permutation 42P3=42×41×40=68880^{42}P_3=42\times41\times40=68880. The first card can be any of 42, the second any of the remaining 41 and the third any of the remaining 40. The figure 1722 is 42×4142\times41, which counts only two draws.

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