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Find the number ways you can choose two distinct integers

Source: MTRP 2019 Class 11-Multiple Choice Question: Problem 5 :-

April 9, 2020

combinatorics

Problem Statement

What is the number of ways you can choose two distinct integers

a

and

b

(unordered i.e. choosing

(a, b)

is same as choosing

(b, a)

from the set

\{1, 2, \cdots , 100\}

such that difference between them is atmost 10, i.e.

|a-b|\leq 10

[*]

{{100}\choose{2}} -{{90}\choose{2}}

[*]

{{100}\choose{2}} -90

[*]

{{100}\choose{2}} -{{90}\choose{2}}-100

[*] None of the above