Total 5040 passwords can be generated when no digits are repeated
• Permutation in mathematics is an arrangement of objects in an definite order. The elements or sets or things are arranged in sequential order or linear order.
• Permutation is classified into four types :
1) where repetition is not allowed
2) where repetition is allowed
3) objects that are non distinct
4) circular permutation
• The formula for calculating permutation is n!/(n-r)!
As we are given that the password uses four digits from 0-9 and repetition is not allowed.
So, n = 10 and r = 4
Using the formula for permutation we get
= 10! / (10-4)!
= 10!/6!
= 10 * 9 * 8 * 7 * 6! / 6!
= 10 * 9 * 8 * 7
= 5040
Therefore, 5040 four digit passwords are possible when no digit is repeated.
Learn more about permutaion here
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