# How many numbers can you make?

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How many numbers can you make ?

How many numbers can you make from given a set of individual digits, and how do make it a greatest number? Let’s take an example to illustrate this concept. Example: -

5 and 8 – In this case, only two sets of numbers is possible – 58 and 85.

**Rule 1 :**If zero(0) is one of the digit then you can not make a smaller number start with zero. So in that case first digit will be the digit which is greater than 0 and less than other given digits.

**Example:**Form all possible three digit number from 0,2 and 6.

**Solution :**As zero is one of the digit but number does not start with zero so next smallest number is 2 so possible numbers are 206,260,602 and 620.

We need to have at least two digits to make a number set.

3, 4, 6 – 346, 364, 436, 463, 634, 643. Here, we have made 6 sets of numbers. Now, in order to get the greatest number we will first see the greatest number in hundredth place i.e. 6, then comes the second greatest number in tens place i.e. 4 and the remaining number in the ones place i.e. 3, and the greatest number is 643. Similarly, for the smallest number we will put the smallest digit in the hundredth place i.e. 3, bigger number in tens place – 4 and the greatest number in the ones place – 6, so the smallest number is 346.

We can create infinite sets of numbers with different digits. However, the number of sets is not dependent on the number of digits given.

**Rule 2 :**The digit in the number should not be repeated unless given more than once or in the question they have mentioned.

2,3,2,4 – 2234, 2324, 2423, 3422, 3224, 3242, 4322, 4232, 4223. Here, we have nine sets of numbers with us, and in these sets only the digit ‘2’ is repeated because it is given twice, and no other digit’s repetition is added.

How many number sets can you create from the following digits?

1, 2, 3, 4, 5.

We can make the following sets of numbers : -

12345, 13452, 14532, 15432, 21345, 21435, 21453, 23451, 23541, 24351, 24531, 24135 and so on… Here, we can see that there can be many number sets that could be made with only these five digits! All we need to do is to create different number sets from the digits given and avoiding the mistake of repeating the number set and repeating the number if not given.

**Rule 3 :**If all the given digits are same : 2, 2, 2, 2. How many number sets can you make from these digits? The answer here surprisingly is only one! Since all the digits are the same, it doesn’t make any difference where you place them or how you place them in a number set.

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