How many 4-digit falling numbers can we make from decimal digits? (A falling number is a positive integer where each digit is larger than the one to its right.)
To find the number of 4-digit falling numbers, we need to consider the possible choices for each digit.
For the first digit, we have 9 choices (1-9), as we cannot choose 0 since it needs to be greater than the digit to its right.
For the second digit, we have 9 choices again (0 is excluded, and the first digit already occupies one of the digits).
For the third digit, we have 8 choices (as we need to exclude the two digits already chosen).
For the fourth digit, we have 7 choices (excluding the three digits already chosen).
To find the total number of falling numbers, we multiply the number of choices for each digit together: 9 * 9 * 8 * 7 = 4,536.
So, there are 4,536 different 4-digit falling numbers that can be made from decimal digits.