Question

a personal identification number that opens a certain lock consists of a sequence of 3 different digits from 0 through 9, inclusive. How many possible PIN are there? (A) 120 (B) 360 C 720 (D) 729 (E) 1,000 ア 172℃

Answer 1

The number of possible PINs is 720.

Step-by-step explanation:

A personal identification number (PIN) that opens a certain lock consists of a sequence of 3 different digits from 0 through 9, inclusive. To find the number of possible PINs, we need to calculate the number of permutations of 3 distinct digits from a set of 10. We can use the formula for permutations, which is given by P(n, r) = n! / (n-r)!. In this case, n = 10 (the number of digits) and r = 3 (the number of positions for the digits).

Using the formula, we get P(10, 3) = 10! / (10-3)! = 10! / 7! = 10 x 9 x 8 = 720.