# Probability: Combination or Permutation?

A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled
thoroughly. Two cards are then removed one at a time from the deck. What is
the probability that the two cards are selected with the number on the first card
being one higher than the number on the second card?

(A) 1/5 (B) 4/25 (C) 1/4 (D) 2/5


My soln.

The card set C = {1,2,3,4,5}

Probability = No. of permutations satisfying (1st>2nd) / Total No. of permutations

Number of permutations satisfying the condition are

{(2,1),(3,1),(3,2),(4,1),(4,2),(4,3),(5,1),(5,2),(5,3),(5,4)} i.e. 10

And the total number of permutations are 5P2 = 20

Hence P = 10/20=1/2

But this is not in the options. What am I missing? Thank you

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You found the probability for the number on the first card being higher than the number on the second card.

But the question asks for the probability for "the number on the first card being one higher than the number on the second card".

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Oh that's really silly of me! Thank you. Had the question mentioned only higher this would have been right? –  segmentation_fault Jan 20 '13 at 8:09
+1; LOL, I misread the question as well... –  Anon Jan 20 '13 at 8:09

Possible Combinations: (5,4), (4,3), (3,2), (2,1) : 4

Total No. of Combinations: 5 x 4 = 20 (without replacement)

Probability : 4/20 = 1/5

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