Mayur travels from Mumbai to Jammu in 7 different ways. But he is allowed to return to Mumbai by any

Question

Mayur travels from Mumbai to Jammu in 7 different ways. But he is allowed to return to Mumbai by any way except the one he used earlier. In how many ways can he complete his journey?

Accepted Answer

{"type":"doc","content":[{"content":[{"marks":[{"type":"bold"}],"text":"Step 1 (Going Journey):","type":"text"},{"type":"text","text":" Mayur has exactly "},{"attrs":{"latex":"7"},"type":"math_inline"},{"text":" different ways to travel from Mumbai to Jammu. Therefore, there are 7 choices for the outgoing trip.","type":"text"}],"type":"paragraph"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 2 (Returning Journey):","type":"text"},{"type":"text","text":" On the return trip, Mayur is allowed to use any of the ways except the one he used to go. This eliminates exactly 1 way, leaving:"}],"type":"paragraph"},{"attrs":{"latex":"7 - 1 = 6 \text{ choices for the return trip}"},"type":"math_block"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3 (Apply Multiplication Principle):","type":"text"},{"text":" Since the choices for going and returning are sequential and independent, we multiply the number of ways:","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"\text{Total ways} = 7 \times 6 = 42"},"type":"math_block"},{"type":"paragraph","content":[{"marks":[{"type":"bold"}],"text":"Step 4 (Conclusion):","type":"text"},{"type":"text","text":" Mayur can complete his journey in exactly "},{"marks":[{"type":"code"}],"text":"42","type":"text"},{"text":" different ways.","type":"text"}]}]}

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