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how many odd no between 300 and 400 are there in which none of digit are repeted

Question

How many odd numbers between 300 and 400 are there in which none of the digits are repeated?

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Solution

To find the number of odd numbers between 300 and 400 in which none of the digits are repeated, follow these steps:

  1. Identify the range: The numbers must be between 300 and 400.

  2. Identify the conditions: The number must be odd and none of the digits can be repeated.

  3. Find the possible digits for each place:

    • The hundreds place is fixed as 3 (since the number must be between 300 and 400).
    • The tens place can be any digit from 0 to 9, except 3 (to avoid repetition). So, there are 9 possible digits.
    • The units place must be an odd digit (to ensure the number is odd). The possible digits are 1, 5, 7, 9. But we've already used 3 in the hundreds place, so there are 4 possible digits. However, we need to exclude any digit that we've used in the tens place. On average, we'll exclude about 1 digit (since each digit has a 1 in 10 chance of being used in the tens place), so there are about 3 possible digits for the units place.
  4. Multiply the number of possibilities for each place: 1 (hundreds place) * 9 (tens place) * 3 (units place) = 27.

So, there are approximately 27 odd numbers between 300 and 400 in which none of the digits are repeated.

This problem has been solved

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