GATE | Sudo GATE 2020 Mock III (24 January 2019) | Question 4

Consider a three digit number abc. Then the probability such that a > b > c is __________ .
(A) 720 / 900
(B) 180 / 900
(C) 120 / 900
(D) 150 / 900


Answer: (C)

Explanation: There are 9∗10∗10=900 three digit numbers.

In the number abc, the digits are strictly decreasing. So they aren’t equal.

From the available ten digits, select any three. This can be done in 10C3 ways.

Now arrange them in descending order. That’s it. We have a favorable number.

So the probability is,

10C3 / 900 = 120 / 900 = 2 / 15 

Option (C) is correct.

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