Question

Suppose we want to choose 3 objects, without replacement, from the 4 objects pencil, eraser, desk, and chair.


(a) How many ways can this be done, if the order of the choices is relevant?


?


(b) How many ways can this be done, if the order of the choices is not relevant?

Answer 1

Answer:24 , 4

Step-by-step explanation:

Given

There are 4 objects

(a)When the order is relevant

We use permutation to get the no of ways, that is

Choosing 3 objects out of 4

$^4P_3=\dfrac{4!}{(4-3)!}=\dfrac{4!}{1!}\\^4P_3=24$

(b) When the order is not important, the same thing can be done in

$^4C_3\ \text{ways}\\\\\Rightarrow \dfrac{4!}{1!3!}=4\ \text{ways}$