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Q14E

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Found in: Page 413

Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

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

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

See the step by step solution

Step 1: Given data

Set positive integer.

Step 2: Concept of Combination

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

Formula:

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

Step 3: Calculation to find a set of two positive integers

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

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

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