Question

How many permutations of three items can be selected from a group of six

Answer 1

Concepts and reason

The concept of permutation is used to solve the problem.

Permutation can be used to find the number of ways a set of objects can be arranged when the set of objects is arranged in an order or a sequence.

Fundamentals

The arrangement of n objects can be calculated by using the formula:

Number of possible arrangement $= n!$

There are n objects, and if r objects are selected at a time when the repetition is not allowed, then the number of possible selections is,

${}^n{P_r} = {\rm{ }}\frac{{n!}}{{\left( {n - r} \right)!}}$

According to the question, three items can be selected from a group of six. Therefore, it can be said that $n = 6$ and $r = 3$ .

The permutation of three items from a group of six can be calculated as:

$\begin{array}{c}\\{}^n{P_r} = \frac{{n!}}{{\left( {n - r} \right)!}}\\\\ = \frac{{6!}}{{\left( {6 - 3} \right)!}}\\\\ = 120\\\end{array}$

Ans:

There are 120 possible ways to arrange three items selected from a group of six.