How many two digit numbers can be formed using these digits without repetition?

The given digits are 1, 2, 3, 4, 5

A two digit number has unit place and 10’s place.

We are given 5 digits (1, 2, 3, 4, 5).

The unit place can be filled (using the 5 digits) in 5 ways.

After filling the unit place since repetition is not allowed one number (filled in the unit place) should be excluded.

So the 10’s place can be filled (using the remaining 4 digits) in 4 ways

∴ Unit place and 10’s place together can be filled in 5 × 4 = 20 ways.

So the number of two-digit numbers = 20

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.

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• How many 4 digit numbers can be formed by using the digit 1 to 9. If repetition of digits is not allowed?
• Similar Questions
• How many 2 digit numbers can be formed from the digits 3 5 7 and 9 if repetition is not allowed?
• How many two digit numbers can be formed using the digit 3/5 7?
• How many 3 digits number can be formed using digits 1 5 7 and 9?
• How many numbers can be formed using the digits 1 3 4 5 6 8 and 9 if I no repetitions are allowed II repetitions are allowed?

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.

nPr = (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.

nCr =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 = 9P4

                           = 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 =  9P5

                                     =   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 

How many 2 digit numbers can be formed from the digits 3 5 7 and 9 if repetition is not allowed?

Summary: All possible two-digit numbers formed by using the digits 3, 7, and 9 if repetition of the digit is allowed are 33, 37, 39, 73, 77, 79, 93, 97, and 99.

How many two digit numbers can be formed using the digit 3/5 7?

Detailed Solution ⇒ Number of possible two-digit numbers which can be formed by using the digits 3, 5 and 7 = 3 × 3. ∴ 9 possible two-digit numbers can be formed.

How many 3 digits number can be formed using digits 1 5 7 and 9?

Solution : 357, 375, 537, 573, 735, 753. Therefore, '6' three-digit numbers can be formed.
Hence, the correct option is (d). Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

How many numbers can be formed using the digits 1 3 4 5 6 8 and 9 if I no repetitions are allowed II repetitions are allowed?

Hence, 64 numbers can be formed.

How many two digit numbers are there in which digits are not repeated?

How many 2

How many two digit numbers can we make using the same digit repeatedly?

How many 2