how many numbers greater than 1000 but not greater than 4000 can be formed with the digits 0,1,2,3,4 . if a. repetition is allowed. b. repetition is not allowed

Question

Answer

The ans is 72 if repetation is not allowed and 375 if repetation is allowed...

Answer

First place can be filled in 3 ways and remaining places can be filled in 125 ways. So total number of ways equal to 3*125 =375

Answer

Finding Numbers Greater than 1000 but not Greater than 4000 with Digits 0, 1, 2, 3, 4

To find the numbers greater than 1000 but not greater than 4000 that can be formed using the digits 0, 1, 2, 3, and 4, we need to consider two scenarios - when repetition is allowed and when repetition is not allowed.

a. When repetition is allowed:

In this scenario, we can use any of the five digits (0, 1, 2, 3, 4) in each of the four positions (thousands, hundreds, tens, and units) of the number.

1. Thousands place:
Since the number must be greater than 1000, the thousands place cannot be 0. Therefore, we have four options: 1, 2, 3, or 4.

2. Hundreds, tens, and units places:
For each of the remaining three positions, we have five options (0, 1, 2, 3, 4) since repetition is allowed.

To find the total number of numbers that can be formed, we multiply the number of options for each position:
4 (options for thousands place) * 5^3 (options for the remaining three positions) = 4 * 5^3 = 4 * 125 = 500.

Therefore, when repetition is allowed, we can form a total of 500 numbers greater than 1000 but not greater than 4000 using the given digits.

b. When repetition is not allowed:

In this scenario, once a digit is used in a position, it cannot be reused in the same number.

1. Thousands place:
Since the number must be greater than 1000, the thousands place cannot be 0. Therefore, we have four options: 1, 2, 3, or 4.

2. Hundreds place:
Since repetition is not allowed, we have four options remaining (0, 2, 3, 4). We cannot use the digit used in the thousands place.

3. Tens place:
Again, since repetition is not allowed, we have three options remaining (0, 2, 3, 4). We cannot use the digits used in the thousands and hundreds places.

4. Units place:
Similarly, we have two options left (0, 2, 3, 4) as repetition is not allowed. We cannot use the digits used in the thousands, hundreds, and tens places.

To find the total number of numbers that can be formed, we multiply the number of options for each position:
4 (options for thousands place) * 4 (options for hundreds place) * 3 (options for tens place) * 2 (options for units place) = 4 * 4 * 3 * 2 = 96.

Therefore, when repetition is not allowed, we can form a total of 96 numbers greater than 1000 but not greater than 4000 using the given digits.

In summary:
a. When repetition is allowed, we can form 500 numbers.
b. When repetition is not allowed, we can form 96 numbers.

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