Question

In how many distinct ways can the digits in the number 2,794,818,731 be arranged? (If there are any zero digits then assume they can be placed in any position)

a) 3,628,800
b) 5,040
c) 362,880
d) 10,000,000

Answer 1

The number of distinct ways the digits in the number 2,794,818,731 can be arranged is 725,760.

Step-by-step explanation:

To find the number of distinct ways the digits in the number 2,794,818,731 can be arranged, we can use the concept of permutations. Since there are no restrictions on the arrangement of the digits and we can assume that zeros can be placed in any position, we can simply find the number of permutations of all the digits.

The number consists of 10 digits, but since there are repeated digits (such as the three 1's and the two 8's), we need to account for the duplication. Using the formula for permutations with repetition, the number of distinct arrangements is given by:

n! / (n1! * n2! * n3! * ...)

where n is the total number of objects and n1, n2, n3, ... are the numbers of each repeated object.

In this case, we have:

n = 10, n1 = 3 (for the repeated 1's), n2 = 2 (for the repeated 8's)

Plugging these values into the formula, we get:

10! / (3! * 2!) = 725,760.

Therefore, the correct answer is 725,760