Question

An automobile dealer provides motorcycles and scooters in three body patterns and $4$ different colors each. The number of choices open to a customer is

• A. ${}^5{C}_3$
• B. ${}^4{C}_3$
• C. $4\times 3$
• D. $4\times 3\times 2$

Answer 1

The correct option is D $4\times 3\times 2$

No. of vehicle options (Motorcycle, scooter)$=2$

No. of body patterns$=3$

No. of different colors$=4$

No. of options for customer=

$\underset{2}{\underset{\downarrow }{\underset{|-------------------|}{No.ofvehicleoptions}}}\underset{X}{\underset{\downarrow }{AND}}\underset{3}{\underset{\downarrow }{\underset{|---------------------|}{No.ofbodypattern}}}\underset{X}{\underset{\downarrow }{AND}}\underset{4}{\underset{\downarrow }{\underset{|------------------------|}{No.ofcolors}}}$

$=4\times 3\times 2$.