# How many 4 digit numbers can be formed by using the digits 1 to 9, if repetition of digits is not allowed?

Permutation is known as the process of organizing the group, body, or numbers in order, selecting the body or numbers from the set, is known as combinations in such a way that the order of the number does not matter.

In mathematics, permutation is also known as the process of organizing a group in which all the members of a group are arranged into some sequence or order. The process of permuting is known as the repositioning of its components if the group is already arranged. Permutations take place, in almost every area of mathematics. They mostly appear when different commands on certain limited sets are considered.

**Permutation Formula**

In permutation r things are picked from a group of n things without any replacement. In this order of picking matter.

^{n}P_{r }= (n!)/(n – r)!Here,

n = group size, the total number of things in the group

r = subset size, the number of things to be selected from the group

**Combination**

A combination is a function of selecting the number from a set, such that (not like permutation) the order of choice doesn’t matter. In smaller cases, it is conceivable to count the number of combinations. The combination is known as the merging of n things taken k at a time without repetition. In combination, order doesn’t matter you can select the items in any order. To those combinations in which re-occurrence is allowed, the terms k-selection or k-combination with replication are frequently used.

**Combination Formula**

In combination r things are picked from a set of n things and where the order of picking does not matter.

^{n}C_{r}=n!⁄((n-r)! r!)Here,

n = Number of items in set

r = Number of things picked from the group

**How many 4 digit numbers can be formed by using the digit 1 to 9. If repetition of digits is not allowed?**

**Answer:**

Repetition of the digit is not allowed. So, for the first digit we have 9 option for second digit we have 8 option for third digit we have 7 option and for fourth digit we have 6 option

There are total 9 digit from which we have to select 4, repetition is not allowed

Total no. of ways =

^{9}P_{4}= 9!/(9-4)!

= 9!/5!

= 3024

**Similar Questions**

**Question 1: How many 5 digit numbers can be formed by using the digit 1 to 9. If repetition of digits is not allowed?**

**Answer:**

Repetition of the digit is not allowed. So, for the first digit we have 9 option for second digit we have 8 option for third digit we have 7 option for fourth digit we have 6 option and for fifth digit we have 5 option

There are total 9 digit from which we have to select 5, repetition is not allowed

Total no. of ways =

^{9}P_{5}

_{ }= 9!/(9-5)!= 9!/4!

= 15,120

**Question 2: How many 3 digit numbers can be formed by using the digit 0,1,2,3. If repetition of digits is allowed?**

**Answer:**

Repetition of digit is allowed. So, for the ones place we have 4 option i.e., 0,1,2,3 similarly for tens place we have again 4 option i.e., 0,1,2,3 and for the hundredth place we have 3 option i.e., 1,2,3 we can’t take 0 at hundredth place because if 0 will be filled at hundredth place it will not become 3 digit number it will be taken as two digit number.

Total no. of three digit number = 3 × 4 × 4

= 48

**Question 3: How many 5 digit numbers can be formed by using the digit 0,1,2,3,4. If repetition of digits is allowed?**

**Answer:**

Repetition of digit is allowed. So, for the ones place we have 5 option i.e., 0,1,2,3,4 similarly for tens place we have again 5 option i.e., 0,1,2,3,4 for the hundredth place we have 5 option i.e., 0,1,2,3,4for the thousandth place we have 5 option i.e., 0,1,2,3,4 and for the ten thousandth place we have 4 option i.e., 1,2,3,4 we can’t take 0 at ten thousandth place because if 0 will be filled at ten thousandth place it will not become 5 digit number it will be taken as 4 digit number.

Total no. of five digit number = 4 × 5 × 5 × 5 × 5

= 2500

**Question 4: How many 4 – digit even numbers can be formed using the digits (3,5,7,9,1,0)** **if repetition of digits is not permitted?**

**Answer:**

For even number unit digit must be 0, Now the remaining digits are 5 i.e., 3,5,7,9,1 now for the thousand place we have 5 option for the hundredth place we have 4 option and for the tens place we have 3 option

Total no. of 4 digits even number can be formed = 5 × 4 × 3

= 60