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Six persons are standing in random order...

Six persons are standing in random order in a aqeue to buy tickets individually. Three of them have a ten rupee note each while the other three have a five rupee note each. The booking clerk has an empty cash box. Find the probability that all the 6 persons will get a ticket each without having to wait. Each ticket costs rupees 5.

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To solve the problem of finding the probability that all 6 persons will get a ticket each without having to wait, we can follow these steps: ### Step 1: Understand the Problem We have 6 persons in a queue: 3 persons have a 10 rupee note (denoted as X) and 3 persons have a 5 rupee note (denoted as Y). Each ticket costs 5 rupees. The booking clerk starts with an empty cash box. For everyone to get a ticket without waiting, the first person in line must have a 5 rupee note, and the last person must have a 10 rupee note. **Hint:** Identify the constraints for the queue arrangement based on the notes each person has. ### Step 2: Identify Valid Arrangements ...
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