How many 6-digit numbers are there in all? (2024)

Hint:
Here, we have to use the concept of permutation for calculating the total number of 6-digit numbers in all. First, we will find the number of choices available for the first place digit of the 6-digit number. Then we will find the number of choices available for the rest of the digits of the 6-digit number by using the permutation. Then by solving this we will get the total number of 6-digit numbers in all.

Complete step by step solution:
It is given that the numbers are the 6 digit numbers.
So, we know that for the first place digits in the 6 digit number there are only 9 choices are available i.e. \[1, 2, 3, 4, 5, 6, 7, 8, 9\] as 0 cannot be in the first place digit because then it will become a 5 digit number.
Therefore, total number of permutation for the first digit in the 6 digit number \[ = {}^9{{\rm{P}}_1} = \dfrac{{9!}}{{{\rm{(9 - 1)}}!}} = 9\]
Now, we know that for the rest of the 5 digits in the 6 digit number there are 10 choices available i.e. \[0,1,2,3,4,5,6,7,8,9\]
Total number of permutation for all the remaining 5 digits in the 6 digit number \[ = {}^{10}{{\rm{P}}_1} = \dfrac{{10!}}{{{\rm{(10 - 1)}}!}} = 10\]
So, total number of 6 digit number in all \[ = 9 \times 10 \times 10 \times 10 \times 10 \times 10 = 900000\]

Hence, there are total \[9,00,000\] 6-digit numbers.

Note:
Permutations may be defined as the different ways in which a collection of items can be arranged. For example: The different ways in which the numbers 1, 2 and 3 can be grouped together, taken all at a time, are \[123,{\rm{ }}132,{\rm{ }}213{\rm{ }}231,{\rm{ }}312,{\rm{ }}321\].
Also we can calculate this using the basic formula
Total 6 digit number \[ = \] Largest 6 digit number \[ - \] Smallest 6 digit number \[ + 1\]
We know that the largest 6 digit number is 999999 and the smallest 6 digit number is 100000.
Therefore, substituting the value, we get
Total 6 digit number \[ = 999999 - 100000 + 1\]
Subtracting the terms, we get
Total 6 digit number \[ = 899999 + 1 = 900000\]
Hence, there are total \[9,00,000\] 6-digit numbers.

How many 6-digit numbers are there in all? (2024)

FAQs

How many 6-digit numbers are there in all? ›

One is the difference (d). The nth term is calculated using the formula. ∴ In total, there are 900,000 6-digit numbers.

How many 6 digit numbers are there in all answers? ›

Answer: There are 9,00,000 (nine lakh) 6-digit numbers in all.

How many 6 digit codes are possible? ›

Or, as @keith points out, the more intuitive way to establish it is simply by knowing that the largest possible 6 figure number is 999,999 (with the lowest being 0) which means there are precisely 1,000,000 possible combinations of a 6 numerical-character string.

How many solutions does a 6 digit code have? ›

The combinations for this problem depends on whether repetition of digits is allowed or not. If repetition is not allowed, then there are 10 * 9 * 8 * 7 * 6 * 5 possible combinations = 151200.

How many outcomes are possible with 6 numbers? ›

But we don't care which order our numbers are picked, and the number of different ways of picking 6 numbers are 6 x 5 x 4 x 3 x 2 x 1 = 6! = 720. Therefore our six numbers are one of 49 x 48 x 47 x 46 x 45 x 44 / 6! = 13983816 so we have about a one in 14 million chance of hitting the jackpot.

How many 6 digit numbers are there in all PDFs? ›

The correct Answer is:900000.

How many 6 digit numbers are there without repetition? ›

600 different numbers will be there.

What are the odds of guessing a 6 digit code? ›

In your example, we can think about it as follows: A six-digit code has 1,000,000 possible states, hence allows for a 1/1,000,000 chance to correctly guess it on the first try.

What is the strongest 6 digit password? ›

There is no “hardest” 6-digit password. Since you specified digits, there are exactly 1,000,000 possible passwords (from “000000” to “999999”), for about 20 bits of entropy. This is insufficient unless there are other strong methods (such as increasing lock-out times) used to prevent guessing attempts.

What is the probability of getting a 6 digit code? ›

The number of total possible codes: n(T): Therefore, the probability of generating 6 digits and the code consisting of 1,2, 3, ... 6 is 0.0466.

What are 6-digit codes? ›

What is a Six-Digit Code? Also referred to as a short code, or six digit phone number, six-digit codes are numbers created by major wireless carriers. These phone numbers allow marketers to communicate with consumers about things like promotional offers, new products and services.

What are the 6-digit numbers? ›

A 6-digit number is like a 10-digit phone except, well, shorter. Instead of using the ten digits, you're familiar with, a 6-digit phone number only uses six. Aside from its length, the only difference is that you can't call a 6-digit number, as it only works for text messaging.

How to calculate possible combinations? ›

How do you find the total number of combinations? To find the total number of combinations of size r from a set of size n, where r is less than or equal to n, use the combination formula: C(n,r)=n!/r!(n-r!)

How many 6 number combinations are there in 49? ›

As long as it doesn't matter which order the numbers are picked in, you have: 49 C 6, or 49 choose 6. Enter this into google and it will tell you: 49 choose 6=13,983,816 different possible combinations of numbers……….

How many 6 number combinations are there from 1 to 50? ›

Thus, if the order does not matter, there are 15890700 ways to select 6 numbers from 50 numbers.

What are the six possible outcomes? ›

When a die is rolled, then the six possible outcomes are 1,2,3,4,5 and 6.

What comes just after 95469999? ›

The number just after 9547999 is 9547999 + 1 = 9548000.

How many 7-digit numbers are there in all solutions? ›

How Many 7-Digit Numbers are there in all? 7-digit numbers start from 1000000 and end with 9999999. There are ninety lakh (90,00,000) 7-digit numbers in all.

How many 5 digit numbers are there in all answer? ›

The smallest 5 digit number is 10,000 and the greatest 5 digit number is 99,999. There are 90,000 five-digit numbers in all. The digit at the ten thousands place in a 5-digit number can never be 0.

What are the most common 6 digit passwords? ›

Here's a list of⁤ the ten most‍ common six​ digit passcodes.
  • 123456.
  • 123456.
  • 1234567.
  • 12345678.
  • 111111.
  • 66666666.
  • 11111111.
  • 1234567890.

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