Math CentralQuandaries & Queries

Question from a parent:

how many four digit numbers can be formed using nos.0,1,2,3 if repetition is allowed?


How many ways can you construct such a number? I am going to start with the leftmost digit, the thousands digit. You have four digits to choose from but if you choose the thousands digit to be 0 hen you don't have a four digit number. For example we wouldn't write 0312 we would instead write 312 and call it a 3 digit number. Hence in the number you are constructing you have 3 choices for the thousands digit.

Once you have chosen a thousands digit, you are allowed repeats so you have 4 choices for the hundreds digit. Thus you have $3 \times 4$ choices for a thousands digit followed by a hundreds digit.

Now you have chosen a thousands digit and a hundreds digit you have again 4 choices for a tens digit and likewise for the units digit.

I hope this helps,

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