Question

How many valid 3 digit numbers can you make using the digits 0, 1, 2 and 3 without
repeating the digits? How about with repeating?

Answer 1

Since there are three places in a 3 digit number _ _ _

At the first place from left we can have only 1,2 and 3 because 0 at that place will not make a valid 3 digit number.

So there can be 3 different values at the first place.

Now, at the second place we can have 4 different values ( 0,1,2,3 ) but since we used one value at the first place and we cannot repeat the digits,so , there can be 3 different values at the second place.

Now, similarly at the third place we can have 4 different values ( 0,1,2,3 ) but since we used two values at the first and second place and we cannot repeat the digits,so , there can be 2 different values at the third place.

So, valid 3 digit numbers you can make using the digits 0, 1, 2 and 3 without repeating the digits =

3 * 3 * 2 = 18

With repeating digts,

At the first place from left we can have only 1,2 and 3 because 0 at that place will not make a valid 3 digit number.

So there can be 3 different values at the first place.

Now, at the second place we can have 4 different values ( 0,1,2,3 ) since we can repeat the digits,so , there can be 4 different values at the second place.

Now, similarly at the third place we can have 4 different values ( 0,1,2,3 ) since we can repeat the digits,so , there can be 4 different values at the third place.

So, valid 3 digit numbers you can make using the digits 0, 1, 2 and 3 with repeating the digits =

3 * 4 * 4 = 48