Question

Introduction to permutations and suppose we want to choose 2 objects, without replacement, from the 5 objects pencil, eraser, desk, chair, and lamp.(a)How many ways can this be done, if the order of the choices is taken into consideration?(b)How many ways can this be done, if the order of the choices is not taken into consideration?

Answer 1

Given

Number of objects = 5

number of objects choosen = 2

Find

a) ways can this be done, if the order of the choices is taken into consideration

b) ways can this be done, if the order of the choices is not taken into consideration

Explanation

a) possible ways =

$\begin{gathered} ^nP_r \\ ^5P_2 \\ \frac{5!}{3!} \\ 20 \end{gathered}$

b) Possible ways =

$\begin{gathered} ^nC_r \\ ^5C_2 \\ \frac{5!}{2!3!} \\ 10 \end{gathered}$

Final Answer

a) 20 ways

b) 10 ways