GATE | GATE CS 2011 | Question 34

A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then removed one at 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


Answer: (A)

Explanation: You have to select 2 cards from 5.

Since the order in which they are drawn matters,
there are 5P2 = 5!/3! = 20 elementary events
from which there are 4 favorable number of cases:

5 before 4, 4 before 3, 3 before 2 and 2 before 1.

Hence, probability = 4/20 = 1/5

Source: http://clweb.csa.iisc.ernet.in/rahulsharma/gate2011key.html

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