Question

how many number can be formed by the digit 1 2 3 4 and 5 if the number is less than 1000 and repetition is allowed for each digit

Answer 1

Answer:

155

Step-by-step explanation:

The condition that the number be less than 1000 just means that we have to choose either 1, 2 or 3 digits.

If we choose 3 digits, there are 5 ways of choosing the first digit, then 5 ways of choosing the 2nd digit (repetition is allowed!), and 5 ways of choosing the third digit.  So in total, there are 5 x 5 x 5 = 125 ways of forming 3 digit numbers.

In much the same way, there are 5 x 5 = 25 ways of forming 2 digit numbers, and 5 ways of forming 1 digit numbers.

So in total there are 125 + 25 + 5 = 155 numbers of the required sort.