Binomial theorem

Question

In the polynomial function f(x) =(x-1)(x²−2)(x³−3)....(x¹¹−11) the coefficient of x⁶⁰ is: ?

Answer 1

C (60,6)  look it up to be 

 

If you multiply out the binomials, you get a 67 term polynomial w power of 66. Why ?

The power of the polynomial is the sum of the powers of the first terms of each binomial.

The sum of numbers 1 to 11  =  11 (12) / 2  [ Gauss's student theorem ]  = 66

The 7th term will have a power of 60

BUT

There is no binomial raised to the power of 66 that equals this polynomial.

So I do not see any solution.

 

Are you sure you got the problem statement correct ??