Question

A train consists of an engine and five cars: I, II, III, IV and V. In...

A train consists of an engine and five cars: I, II, III, IV and V. In how many ways can the cars be arranged so that car I is closer to the engine than car II?

Math   Statistics-And-Probability   
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Answer #1

Number of ways the car can be arranged so that car I is closer than car II when it is in first position =1*4!=24

Number of ways the car can be arranged so that car I is closer than car II when it is in second position=3*1*3!=18

Number of ways the car can be arranged so that car I is closer than car II when it is in third position=3*2*1*2!=12

Number of ways the car can be arranged so that car I is closer than car II when it is in fourth position=3*2*1*1*1=6

Number of ways the car can be arranged so that car I is closer than car II =24+18+12+6=60

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