In how many ways can these digits in a number 8,555,111 be arranged
7!/(3!3!)
Review permutations with duplicates
There are 140 ways to do this.
Well, let me do a quick calculation...
There are 7 digits in total - 3 fives, 3 ones, and 1 eight.
To find the number of ways these can be arranged, we can use the formula for counting permutations.
The number of ways the digits can be arranged is calculated as:
7! / (3! * 3! * 1!) = 840
So, there are 840 different ways to arrange the digits in the number 8,555,111.
That's a lot of combinations! Just imagine all the different phone number possibilities you could have with those digits.
To find the number of ways the digits in the number 8,555,111 can be arranged, we need to determine the total number of permutations.
The given number has 8 digits, with the following frequency of digits:
- 3 x 1's
- 3 x 5's
- 2 x 8's
The formula to calculate the number of permutations is as follows:
Number of permutations = (Total number of digits)! / (Frequency of each digit1! * Frequency of each digit2! * ... * Frequency of each digit n!)
Plugging in the values, we get:
Number of permutations = (8!) / (3! * 3! * 2!)
Calculating each factorial:
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320
3! = 3 * 2 * 1 = 6
3! = 3 * 2 * 1 = 6
2! = 2 * 1 = 2
Substituting these values back into the equation:
Number of permutations = 40,320 / (6 * 6 * 2)
Simplifying further:
Number of permutations = 40,320 / 72
Number of permutations = 560
Therefore, there are 560 ways the digits in the number 8,555,111 can be arranged.
To find out in how many ways the digits in the number 8,555,111 can be arranged, you can use the concept of permutations.
A permutation is an arrangement of items in a specific order, where the order matters. In this case, the order of the digits matters since we are arranging them.
To calculate the number of permutations, you can use the formula for permutations of a set, which is:
P(n, r) = n! / (n - r)!
In this formula, n represents the total number of items in the set (in this case, the number of digits), and r represents the number of items being arranged (in this case, all the digits).
Substituting the values into the formula:
P(7, 7) = 7! / (7 - 7)!
= 7! / 0!
The factorial of a number (n!) is the product of all positive integers from 1 to n. In this case, 7! is calculated as:
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1
= 5040
Since anything divided by 0 is undefined, we cannot divide 7! by 0!. However, it is important to note that any number divided by 0 is considered infinite. Therefore, the number of ways the digits in the number 8,555,111 can be arranged is infinitely large.