In the expansion of (x+1)^42 what is the coefficient of the x^2 term?

In the expansion of (x+1)^42 what is the coefficient of the x^2  term?

=861x^2

In (x+1)^42, 42^2 multiplications take place.

The relevant multiplications in this case are those that are x * x * 1^40 (= x * x * 1 = x^2)

So in each of the relevant multiplication, 2 x terms are multiplied and 40 "1" terms are multiplied.

This can be modeled onto a combinations problem of how many different ways there are to take 2 objects (x terms) from a group of 42 unqiue objects.

I don't know how to solve this, but I do know how to model it, so hopefully someone can take over from here.

The coefficients are simply the binomial coefficients of: 42C1, 42C2, 42C3...........42C42.