Answer:
Therefore, the total number of ways the 7-digit number can be formed is given by:
7! / (2! * 2!)
Simplifying the expression:
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040
2! = 2 * 1 = 2
Substituting the values into the expression:
5040 / (2 * 2) = 5040 / 4 = 1260
Therefore, the number of ways a 7-digit number can be formed using the given digits is 1260.
Among the provided answer choices, none of them matches the correct result of 1260.
Explanation:
To determine the number of ways a 7-digit number can be formed using the digits 2, 2, 2, 3, 3, 4, and 5, we need to consider the permutations of these digits while accounting for the repeated digits.
Step 1: Find the total number of permutations of all 7 digits.
Since all 7 digits are distinct, we can calculate the number of permutations of 7 digits: 7!.
Step 2: Adjust for the repeated digits.
In this case, we have two repeated digits (2, 2) and (3, 3). To account for these repetitions, we divide the total number of permutations by the factorial of the repetition count for each digit.
For the digit 2, we have two repetitions, so we divide by 2!.
For the digit 3, we also have two repetitions, so we divide by 2!.