How many integer solutions does this expression have:

x1*x2*3*x4 = 770

So, 2*5*7*11 = 770

But the catch is that either one, two, or three of these variables can be 1 as well.

So, 70*11*1*1 = 770

Similarly, 770*1*1*1 = 770.

The way I proceeded with this question, was a follows:

i) No "1": Number of cases = 4! = 24

ii) One "1": Number of cases = C(4,3)*4! = 96

iii) Two "1": Number of cases = C(4,2)*4!/2! =72

iv) Three "1": Number of cases = 4

So, total = 24 + 96 + 72 + 4 = 196

However, I believe (not 100% sure) that the correct answer is 256.

Where am I going wrong

x1*x2*3*x4 = 770

So, 2*5*7*11 = 770

But the catch is that either one, two, or three of these variables can be 1 as well.

So, 70*11*1*1 = 770

Similarly, 770*1*1*1 = 770.

The way I proceeded with this question, was a follows:

i) No "1": Number of cases = 4! = 24

ii) One "1": Number of cases = C(4,3)*4! = 96

iii) Two "1": Number of cases = C(4,2)*4!/2! =72

iv) Three "1": Number of cases = 4

So, total = 24 + 96 + 72 + 4 = 196

However, I believe (not 100% sure) that the correct answer is 256.

Where am I going wrong

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