# How many numbers without repetition can be formed by use of digits 1, 2, 3, 4, 5, and 6?

**Talent34**- 6 Answers

For 6 digit numbers:

You can choose any of the 6 digits for the first place, then 5 of the digits for the second place and 4 for the third place, etc. So the number of 6 digit numbers you can form is 6 x 5 x 4 x 3 x 2 x 1 = 720

For 5 digit numbers:

You can choose any of the 6 digits for the first place, then 5 of the digits for the second place and 4 for the third place, etc. So the number of 5 digit numbers you can form is 6 x 5 x 4 x 3 x 2 = 720

For 4 digit numbers:

You can choose any of the 6 digits for the first place, then 5 of the digits for the second place and 4 for the third place, etc. So the number of 4 digit numbers you can form is 6 x 5 x 4 x 3 = 360

For 3 digit numbers:

You can choose any of the 6 digits for the first place, then 5 of the digits for the second place and 4 for the third place. So the number of 3 digit numbers you can form is 6 x 5 x 4 = 120

For 2 digit numbers:

You can choose any of the 6 digits for the first place, then 5 of the digits for the second place. So the number of 2 digit numbers you can form is 6 x 5 = 30

For 1 digit numbers:

You can choose any of the 6 digits So the number of 1digit numbers you can form is 6

Adding these together gives 720 + 720 + 360 + 120 + 30 + 6 = 1956

This is called a permutation without repetition. In Math Permutation means that you care about the order, in our case 123,456 is a different number than 123,546. Without repetition means that we aren't allowed to use the digit "1" more than once. To calculate how many numbers we can make we multiple our number of choices for each place holder. When we choose the first digit of a number we have six choices, when we choose the second digit we have 5, and so on. To get the answer then we multiple 6x5x4x3x2x1. This is represented by the symbol "!" which is the factorial function. When you see 6! in math it just means 6x5x4x3x2x1. In this case 6! = 720. So there are 720 different numbers we can make without repetition of the digits 1-6.

...You have the ability to create a number with 1 digit, 2 digits, 3 digits, etc. from these 6 integers. Therefore, for a 1 digit number you can create 6. For a 2-digit number you can create 6*5=30, for a 3-digit you can create 6*5*4=120, a 4-digit: 6*5*4*3=360, a 5-digit: 6*5*4*3*2=720, and a 6-digit: 6*5*4*3*2*1=720.

SUmming these gives: 720+720+360+120+30+6=1956.

6 digits can be chosen for the first place, 5 for the second place, 4 for the third place, 3 for the fourth place, 2 for the fifth place and one for the sixth place. Therefore total number of permutations is 6 x 5 x 4 x 3 x 2 x 1 = 720

Therefore 720 different six digit numbers can be formed from the digits 1, 2, 3, 4, 5 and 6.