How many 4 digit numbers can be made using 0-7 with no repeated digits allowed?
To form a four-digit number, we can't use 0 as the first digit since it would result in a three-digit number. Therefore, we have seven options for the first digit (1-7).
After choosing the first digit, we have six remaining options (0 and 7 cannot be used again). For the second digit, we have six choices available.
Similarly, for the third digit, we have five options left (excluding the two digits already chosen), and for the last digit, we have four choices.
Hence, the total number of four-digit numbers with no repeated digits is calculated as:
7 choices for the first digit × 6 choices for the second digit × 5 choices for the third digit × 4 choices for the fourth digit
Therefore, there are 7 × 6 × 5 × 4 = <<7*6*5*4=840>>840 four-digit numbers that can be formed using the digits 0-7 without repetition.
To find the number of 4-digit numbers that can be made using the digits 0-7 with no repeated digits allowed, we can use the concept of permutations.
Since we have 8 digits (0-7) to choose from for each of the 4 positions, the total number of 4-digit numbers without any restrictions is 8 * 8 * 8 * 8 = 4096.
But since we cannot repeat any of the digits, we need to subtract the number of cases where the digits are repeated.
For the first digit, we have 8 choices.
For the second digit, we have 7 choices (as we have already used 1 digit).
For the third digit, we have 6 choices (as we have already used 2 digits).
For the fourth digit, we have 5 choices (as we have already used 3 digits).
So, the total number of 4-digit numbers that can be made using the digits 0-7 with no repeated digits allowed is 8 * 7 * 6 * 5 = 1,680.