The number of ways in which we can choose 2 distinct intege…

Maths Permutations & Combination Definition of Combinations, Condition Combinations, Division into Groups, Derangements Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 14, 2026

The number of ways in which we can choose 2 distinct integers from 1 to 100 such that the difference between them is at most 10 is-

100 C 2 – 90 C 2

100 C 98 – 90 C 88

100 C 2 – 90 C 88

None of these

Text Solution

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The correct answer is:

CHECK THE SOLUTION.

(a, b, c )

Let the chosen integers be x 1 and x 2

Let there be a integer before x 1 , b integer between x 1 and x 2 and c integer after x 2 .

∴ a + b + c = 98. Where a ≥ 0, b ≥ 10, c ≥ 0

Now if we consider the choices where difference is at least 11, then the number of solution is 88+3–1 C 3–1 = 90 C 2

∴ The number of ways in which b is less than 10 is 100 C 2 – 90 C 2 which is equal to , and option.

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