How many number of four digits can be formed with the digits 1, 3… - Vidyadip

Question

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

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Answer

Total number of digits = 4 Total number of 4 digit numbers $=\frac{4!}{2!}$ But, zero cannot be first digit of the four digit numbers. $\therefore$ Total number of 3 digit numbers $=\frac{3!}{2!}$ $\therefore$ Total number of numbers $= \frac{4!}{2!}-\frac{3!}{2!}$ $=\frac{4\times3\times2!}{2!}-\frac{3\times2!}{2!}$ $=12-3$ $=9$ Hence, total number of four digit numbers = 9.

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