Apersonal identification number (pin) 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

720 possible PIN can be generated.

Explanation:

To calculate different number of orders of digits to create password and PIN, we calculate permutation.

Permutation is a term that means the number of methods or ways in which different numbers, alphabets, characters and objects can arranged or organized. To calculate the permutation following formula will be used:

nPr = n!/(n-r)!

there P is permutation, n is number of digits that need to be organize, r is the size of subset (Number of digits a password contains)

So in question we need to calculate

P=?

where

n= 10   (0-9 means total 10 digits)

r= 3     (PIN Consist of three digits)

So by using formula

10P3 = 10!/(10-3)!

        =10!/7!

        = 10x9x8x7!/7!

        = 10x9x8

        = 720