Matt C. answered • 09/27/21
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PhD in Mathematics taught Finite Math at University of Montana
Hello, the answer is 2520.
To see why, consider the five digits of the number.
For the leftmost digit, there are 7 options (1, 2, 4, 6, 7, 8, 9).
For the second digit, there are 6 options (all but the first chosen one, whatever it was).
For the third digit, there are 5 options.
For the fourth digit, there are 4 options
For the fifth (rightmost) digit, there are 3 options remaining.
By the multiplication principle, this means the total number of options is 7 * 6 * 5 * 4 * 3 = 2520.
Matt C.
Hi, I am glad the answer was helpful. I did not see the second part before. For the number to be less than 50000, the first digit must be either 1, 2, or 4. So there are only 3 options for the leftmost digit. But still 6 for the second, 5 for the third, 4 for the fourth, and 3 for the fifth. So the total is 3 * 6 * 5 * 4 * 3 = 1080.
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09/27/21
Kaylen C.
Okay thank you! I understand that completely. What about the second question? I am still having trouble figuring out how to answer it.09/27/21