Q.1.3 - A First Course in Probability

Question

In how many ways can$r$ objects be selected from a set of $n$objects if the order of selection is considered relevant?

Step-by-Step Solution

Answer

Choose the first, then the second, and so on...

$\frac{n!}{(n-r)!}$

Step 1 Given Information.

$r$ objects are selected from a set of $n$objects if the order of selection is considered relevant.

Step 2 Explanation.

Choosing$r$ from$n$, ordered

The first element can be selected in $n$ways

The second can be any of the remaining $n-1$

The $r$element can be any of the$n-r+1$ elements.

By the generalized principle of the product, there are$n·(n-1)·\dots (n-r+1)=\frac{n!}{(n-r)!}$ possible choices.