What is the coefficient of the x7y3 term in the expansion of (x + y)10

If you do it by Pascal's Triangle:

Row 0:    1

Row 1:    1  1

Row 2:    1  2  1

Row 3:    1  3  3  1

Row 4:    1  4  6  4  1  

Row 5:    1  5  10  10  5  1

Row 6:    1  6  15  20  15  6  1

Row 7:    1  7  21  35  35  21  7  1

Row 8:    1  8  28  56   70 ...

Row 9:    1  9  36  84  126  ...

Row 10:  1  10  45  120  210 ...   <--->  1x^10 + 10x^9y^1 + 45x^8y^2 + 120x^7y^3

If you do it by combinations, you want  10nCr7 = 120  

(the 10 comes from row 10, determined by the sum of the two exponents, the 7 comes from the exponent of the x-term).