Question

suppose we want to choose 2 objects, without replacement, from the 3 objects pencil, eraser, and desk. (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 choices is not taken into consideration?

Answer 1

`\begin{gathered} we\text{ want to choose 2 objects without replacement, from 3 objects:} \\ \text{pencil, eraser, desk} \\ a)\text{ the first object can be choosen in 3 ways,} \\ \text{the second can be choosen in 2 ways} \\ \\ \text{hence there are 3.2=6 ways} \end{gathered}`
`\begin{gathered} b)i\text{ f the order is not taken into account, there are} \\ C^3_2=(3!)/(2!(3-2)!)=(6)/(2\cdot1)=3 \\ \text{where } \\ C^3_2\text{ are the combination of 3 object taken in 2 } \end{gathered}`