Question

Which rule must be used to find the number of strings of four decimal digits that do not contain the same digit twice?

O the division rule
O the sum rule
O the product rule
O the subtraction rule

Answer 1

The rule that must be used to find the number of unique strings of four decimal digits where the same digit does not appear twice is the product rule. By multiplying the possibilities for each digit's placement, we can calculate the total number of such strings.

Step-by-step explanation:

To find the number of strings of four decimal digits in which the same digit does not appear twice, we must use the product rule of combinatorics. This rule states that if one event can occur in 'm' ways and a second can occur independently in 'n' ways, then the two events can occur in 'm x n' ways. Let's apply this rule:

1. The first digit can be any of the 10 digits from 0 to 9, so there are 10 ways.
2. The second digit can be any of the remaining 9 digits, so there are 9 ways.
3. The third digit can be chosen from the remaining 8 digits, so there are 8 ways.
4. Finally, the fourth digit can be chosen from the remaining 7 digits, giving us 7 ways.

We multiply these possibilities together (10 x 9 x 8 x 7) to find the total number of unique four-digit strings where no digit is repeated.