Question

In how many ways can a set of two positive integers less than 100be chosen?

Short answer

There are 4851 ways can a set of two positive integers less than 100 be chosen.

Step-by-step solution

Given data

Set positive integer.

Concept of Combination

A combination is a selection of items from a set that has distinct members.

Formula:

${}_{\mathbf{n}}{\mathbf{C}}_{\mathbf{r}}\mathbf{=}\frac{\mathbf{n}\mathbf{!}}{\mathbf{r}\mathbf{!}\mathbf{(}\mathbf{n}\mathbf{-}\mathbf{r}\mathbf{)}\mathbf{!}}\mathbf{\mid }$

Calculation to find a set of two positive integers

A set of two positive integers less than 100 be chosen as:

$\begin{array}{r}C(99,2)=\frac{99!}{(2!\times 97!)}\\ C(99,2)=4851\end{array}$

Thus, there are 4851 ways can a set of two positive integers less than 100 be chosen.