Question

Suppose we want to choose 2 colors without replacement from the 3 colors

Answer 1

Question:

Suppose we want to choose 3 colors, without replacement, from the red, blue, green, and purple.

(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:

(a) 6 choices

(b) 3 Choices

Step-by-step explanation:

Given:

3 Colors

Order of choice : Red, Blue, Green

(a) Order of the choices taken into consideration :

When we are picking  the first colour there are 3 color choice.

When we are picking second colour there are 2 choice and so on.

Therefore, total choices are = 3*2 = 6 choices

(b) Order of the choices not taken into consideration :

When to take this option we choose as $3 \times 2$  and the remove the duplicates

Therefore, choices are = $\frac{(3 \times 2)}{(1 \times 2)}$ =$\frac{6}{2}$ = 3 Choices