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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