Answer:
<u>720</u> 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
Given, a = 3, r = 1/2, n = 10
%r is common ratio
%n is number of terms
%a is the first term of the series
Sum = 0;
a = 3;
r = 1/2;
for i = 0 : 1 : 10;
Sum = Sum + a * r ^ i;
end
Sum
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