A 4 digit number is to be selected at random from the numbers 0 to 9 with no repetition of digits. How many arrangements can there be?
I keep getting 5040 by doing 10 x 9 x 8 x 7 but the answers say 4536 ways. I dont know what I am doing wrong.
the first digit cannot be zero. That leaves
9*9*8*7 = 4536
Ahh yes forgot about zero. Thanks heaps
To find the number of arrangements for a 4-digit number with no repetition of digits, you can follow these steps:
Step 1: Determine the options for the first digit.
Since no repetition of digits is allowed, there are 10 options (0 to 9) for the first digit.
Step 2: Determine the options for the second digit.
After choosing the first digit, there are 9 remaining options for the second digit. (10 - 1 used digit)
Step 3: Determine the options for the third digit.
After choosing the first and second digits, there are 8 remaining options for the third digit. (10 - 2 used digits)
Step 4: Determine the options for the fourth digit.
Finally, after choosing the first three digits, there are 7 remaining options for the fourth digit. (10 - 3 used digits)
Now, to find the total number of arrangements, you need to multiply the number of options for each digit together:
10 (options for the first digit) * 9 (options for the second digit) * 8 (options for the third digit) * 7 (options for the fourth digit) = 5,040.
Therefore, based on your calculations, you are correct that there should be 5,040 arrangements.
If the answer key states that there are 4,536 arrangements instead, there might be a mistake in the answer key. Double-check the problem statement and consider discussing it with your instructor or classmates to resolve any confusion.