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Find the total number of ways to form a 3 digit number(without repetition) from the digits 0,1,2, ..., 5.5 + ⁵P₂⁶P₃5 x ⁵P₂4 x ⁴P₂

Question

Find the total number of ways to form a 3 digit number (without repetition) from the digits 0, 1, 2, ..., 5.

5.5+5P26P35×5P24×4P2 5.5 + ⁵P₂⁶P₃5 \times ⁵P₂4 \times ⁴P₂

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Solution

The question seems to be asking for the total number of ways to form a 3-digit number without repetition from the digits 0,1,2,3,4,5.

Step 1: We have to form a 3-digit number, and the first digit can't be 0 (as it wouldn't be a 3-digit number then). So, we have 5 choices (1,2,3,4,5) for the first digit.

Step 2: For the second digit, we can't use the first digit again, but we can use 0 this time. So, we have 5 remaining choices (0 and four from 1,2,3,4,5 excluding the first digit).

Step 3: For the third digit, we can't use the first and second digits. So, we have 4 remaining choices.

So, the total number of ways to form a 3-digit number is 5 (choices for the first digit) * 5 (choices for the second digit) * 4 (choices for the third digit) = 100 ways.

The part "5.5 + ⁵P₂⁶P₃5 x ⁵P₂4 x ⁴P₂" seems to be unrelated or incorrectly formatted, as it doesn't fit into the context of the question.

This problem has been solved

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