Question

O COUNTING AND PROBABILITY Introduction to permutations and combinations Suppose we want to choose 2 colors, without replacement, from the 5 colors red, blue, green, purple, and yellow. (a) How many ways can this be done, if the order of the choices is taken into consideration? X Х ? (b) How many ways can this be done, if the order of the choices is not taken into consideration?

Answer 1

Answer: We are given five colors, Red Blue Green Purple and Yellow, We need to place them into two, and would like to know the total combinations, A The order matters, B Order does not Matter.

A-The order matters:

`\begin{gathered} \text{slots =2 } \\ \text{Colors = =5} \end{gathered}`

Therefore we have:

`5\cdot4\cdot3\cdot2\cdot1=60\cdot2\cdot1=120\text{ ways}\rightarrow\text{ Because order mattered}`

B-The order does not matter:

`(5!)/(2!)=(5\cdot4\cdot3\cdot2\cdot1)/(2\cdot1)=60\rightarrow Because\text{ the order does not matter}`

Note!, When the order does matter, we are counting each possibility twice, and when it does not, we only count once.