How many six digit numbers greater than 700 000 can be made from the digits 2, 2, 4, 4, 4, 7?

A. 10
B. 60
C. 64
D. 120

If it has to be greater than 700000, the first digit must be 7. That leaves us with 5 digits 2,2,2,4,4 to make the remainder of the number.

Here we have 5 digits of which 2 and 3 are identical, so the number of ways to choose the 5 digits is
C(5,3,2) = 5!/(3!2!)
I'll let you do the rest.

To find the solution to this problem, we can break it down into steps.

Step 1: Determine the possible choices for the first digit.
The first digit has to be greater than 7 since we want the number to be greater than 700,000. The only option available is 7.

Step 2: Determine the possible choices for the second digit.
The second digit can be any of the remaining digits: 2, 2, 4, 4, 4, 7.
Since the two digits 2 and 7 are repeated, we need to consider them as separate cases.

Case 1: The second digit is 2.
In this case, we have two 2s left to choose from, and the remaining digits are 4, 4, 4, and 7. Therefore, we have 4 choices for the second digit.

Case 2: The second digit is 7.
In this case, we have one 7 left to choose from, and the remaining digits are 2, 2, 4, and 4. Therefore, we have 4 choices for the second digit.

So, in total, we have 4 choices for the second digit.

Step 3: Determine the possible choices for the third digit.
The third digit can be any of the remaining digits: 2, 2, 4, 4, 4, 7.
Again, we need to consider the repeated digits separately.

Case 1: The third digit is 2.
In this case, we have one 2 left to choose from, and the remaining digits are 4, 4, 4, and 7. Therefore, we have 4 choices for the third digit.

Case 2: The third digit is 4.
In this case, we have three 4s left to choose from, and the remaining digits are 2, 2, and 7. Therefore, we have 3 choices for the third digit.

Case 3: The third digit is 7.
In this case, we have one 7 left to choose from, and the remaining digits are 2, 2, 4, and 4. Therefore, we have 4 choices for the third digit.

So, in total, we have 4 choices for the second digit.

Step 4: Determine the possible choices for the remaining digits.
For the fourth, fifth, and sixth digits, we can repeat the same logic used in Step 3 since we have the same digits available. In each case, we have 3, 2, and 4 choices respectively.

Step 5: Calculate the number of possible six-digit numbers.
To find the total number of possible six-digit numbers, we need to multiply the number of choices for each position together.
4 choices for the second digit × 4 choices for the third digit × 3 choices for the fourth digit × 2 choices for the fifth digit × 4 choices for the sixth digit = 1,152

Therefore, the correct answer is not given among the options provided. The correct answer is 1,152.