Solution
- This is a combination question because we are to choose from a list of items in a distinct lineup.
- The formula for combination is:
[tex]\begin{gathered} ^nC_r=\frac{n!}{(n-r)!r!} \\ \\ where, \\ n\text{ is the total amount of items} \end{gathered}[/tex]- Also, since the choice or distinct arrangement of the cars independent, we can simply multiply the possible combinations.
- That is,
[tex]\begin{gathered} \text{ Convertible:} \\ ^{20}C_7=77520 \\ \\ \text{ SUV:} \\ ^{10}C_5=252 \\ \\ \text{ Vans:} \\ ^8C_3=56 \end{gathered}[/tex]- Thus, the possible number of distinct line ups is:
[tex]77520\times252\times56=1,093,962,240\text{ line ups}[/tex]