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Worked solution

Add the air and sea travel alternatives

One can travel from Singapore to Tokyo by air and sea. If there are 4 passenger airlines and 3 passenger shipping lines operating between the 2 cities, what is the total number of ways a man can travel from Singapore to Tokyo?

CJC · Lecture · Example 1

Count each mutually exclusive alternative

Number of ways by air=4. Number of ways by sea=3. As the source solution shows, the intended journey uses one air service or one sea service, not both in sequence.

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Add the two counts

Total number of ways=4+3=74+3=7. The diagram has four air arrows and three sea arrows between the same two cities.

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Source route construction from Singapore to Tokyo: four air arrows and three sea arrows are alternatives, not successive legs. Choose one route, giving four plus three equals seven. Photographs and national flags are represented by city and mode labels.
Source route construction from Singapore to Tokyo: four air arrows and three sea arrows are alternatives, not successive legs. Choose one route, giving four plus three equals seven. Photographs and national flags are represented by city and mode labels.
Source route construction from Singapore to Tokyo: four air arrows and three sea arrows are alternatives, not successive legs. Choose one route, giving four plus three equals seven. Photographs and national flags are represented by city and mode labels.

Common mistakes

The source phrase by air and sea describes the two available modes. The printed solution treats them as alternatives, so add rather than multiply.

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