# How many numbers of four digits can be formed with the digits 1, 3, 3, 0?

Given, the numbers 1, 3, 3, 0. Total of 4 digits, and it has 1 repeated digit 1 repeated twice.

To find: Number of four digit numbers that can be formed using digits 1, 3, 3, 0. Notice that an arrangement in which digit 0 in the first place will not be counted as four digit number. For example- 0331 will not be counted as four digit number since it is a 3 digit number.

The problem can now be rephrased as to find a total number of permutations of 4 objects (1, 3, 3, 0) of which two objects are of same type (1, 1), And all other objects are distinct. But, 0 cannot be in first place (Condition of four digit number).

First, we will find a total number of permutations of these 4 digits and then we will go minus all those permutations in which 0 will come in first place. This will give us exactly number of four-digit numbers that can be formed by permuting the given digits, i.e. 1, 3, 3, 0.

Total number of permutations will be Number of permutations in which 0 will come at the first place will be equal to (Number of ways we can arrange the remaining digits, i.e. 1, 3, 3 in the remaining three places) Total number of permutations of given digits forming a four-digit number is equal to   Hence, total number of permutations of 4 digits (1, 3, 3, 0) forming a 4 digit number is 9.

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