[ Rule of product ] [ Decimal number system ]

How many four-digit numbers can be formed using the digits 1, 2, 3, 4, and 5, if:

a) no digit is repeated more than once;

b) repetitions of digits are allowed

c) the numbers must be odd and no digits should be repeated?
a) the first digit can be chosen in 5 ways, the second in 4 ways, and so on.

b) Each digit can be chosen in 5 ways

c) Starting from the end: the units digit can be chosen in 3 ways, the tens digit in 4 ways, the hundreds digit in 3 ways, ...

## Answer

a) $5 \cdot 4 \cdot 3 \cdot 2=120$;
b) $5^{4}=625$ numbers;
c) $3 \cdot 4 \cdot 3 \cdot 2=72$ numbers.

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