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

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=(4!)/((4-3)!)=(4!)/(1!)\\^4P_3=24`

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

`^4C_3\ \text{ways}\\\\\Rightarrow (4!)/(1!3!)=4\ \text{ways}`