Question

How many 4 digit numbers can be formed using the digits 0 1 2 3 4 5 with repetition?

Answer 1

infinite numbers can be formed using these digits.......

Answer 2

Answer:To start with, lets break the problem into two cases, for simplicity sake,

When we have 0(zero) in the units place

When we do not have 0(zero) in the units place

Case #1:

Since we have a zero units place, all such numbers would be even numbers.

This question requires that the numbers be formed without repetition of digits. If such is the restriction, since we are left with 1,2,3,5,6

Thousands place can be filled up in 5ways, any one of the 1,2,3,5,6.

for example, 3 in thousands place looks like this. Similarly we can have any number from the set of 1,2,3,5,6 which can take up this thousands place.

Hundred’s place can be filled up in 4ways, since we already used one of the digits to fill up thousands place.

for example, 5 in hundreds place looks like this. Similarly we can have any number from the set 1,2,3,5,6 except the one used in thousands place.

Lastly, Ten’s place can be filled up in 3ways, since we have already used two digits, one digit in thousands place and another digit in hundred’s place.

continuing the previous example, 2 in ten’s place,

So with zero in units place,

Thousands place can be filled up in 5ways

Hundred’s place can be filled up in 4ways

and Ten’s place can be filled up in 3ways

giving us, 5∗4∗3 i.e 60 such numbers, with the number 3520 being one among them.

Moving to the second case, case #2, where the units place can be filled up by any pone of the digits 2 or 6.

Units place can be filled up in 2ways, one among 2 or 6 (zero in units place was covered separately).

for example, with 2 in units place, we have

Thousands place can be filled up in 4ways, any one of the 1,3,5,6. With zero in thousands place, the number under consideration turns into three digit number.

for example, 3 in thousands place looks like this. Similarly we can have any number from the set of 1,3,5,6 which can take up this thousands place.

Hundred’s place can be filled up in 4ways, from the set 0,1,5,6. since we already used two digits to fill up thousands and units place. (We can have zero in hundreds place).

for example, 0 in hundreds place looks like this. Similarly we can have any number from the set 1,2,3,5,6 except the one used in thousands place.

Finally, Ten’s place can be filled up in 3ways, since we have already used three digits, in thousands place, hundred’s place and units place.

continuing the previous example, 6 in ten’s place,

So with non-zero digit in units place,

Thousands place can be filled up in 4ways

Hundred’s place can be filled up in 4ways

Ten’s place can be filled up in 3ways

and Units’s place can be filled up in 2ways.

giving us, 4∗4∗3∗2 i.e 96 such numbers, with the number 3062 , discussed as an example, being one among them.

Summing up the results in case #1 and case #2, we can have 156 4-digit even numbers that can be formed using 0,1,2,3,5,6 without repetition.

I hope my explanation is simple and clear.

Step-by-step explanation: