In how many times can the number 9,633,333 be arranged
You are arranging 7 items of which 5 are the same
number of cases = 7!/5! = 42
To calculate the number of arrangements of the digits in 9,633,333, we need to consider that there are a total of 8 digits in the number, including 6 digits of the number 3 and 2 digits of the number 9.
The formula for calculating the number of arrangements of n objects, where there are p1 objects of one type, p2 objects of another type, and so on, is given by:
n! / (p1! * p2! * ...)
In this case, n = 8, p1 = 6, and p2 = 2.
Applying the formula, we have:
8! / (6! * 2!)
Calculating the factorials:
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
2! = 2 x 1 = 2
Substituting the values into the formula, we get:
40,320 / (720 * 2)
Simplifying the expression:
40,320 / 1,440
The number of arrangements of 9,633,333 is approximately:
40,320 / 1,440 = 28
Therefore, the number 9,633,333 can be arranged in 28 different ways.
To determine the number of ways that the digits in the number 9,633,333 can be arranged, we need to count the total number of digits and consider any repeated digits.
The number 9,633,333 has a total of 7 digits.
Now, we have to consider the repeated digit: 3 appears four times in the number.
To calculate the number of arrangements, we can use the formula to account for repeated digits:
n!/ (r1! * r2! * ... * rk!)
Where n is the total number of digits, and r1, r2, ..., rk represent the number of repetitions for each digit.
In this case, n = 7 and r1 = 4 (since 3 repeats four times).
Substituting these values into the formula, we get:
7! / (4!)
To simplify the equation further, we calculate the factorials:
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040
4! = 4 * 3 * 2 * 1 = 24
Plugging these values into the formula, we get:
5,040 / 24 = 210
Therefore, the number 9,633,333 can be arranged in 210 different ways.