Binomial Theorem (urgent)

(1+x)^7(1+x)^8
=( Σ7Cr*x^r)( Σ8Cs*x^s)
The general term of r+s
=(7Cr)(8Cs)x^(r+s)
let r+s=7
the possibile answers are
0,7
1,6
2,5
...
7,0
the coefficient of x^7
=(7C0)(8C7)+(7C1)(8C6)+...+(7C7)(8C0)
=8+196+21*56+35*70+35*56+21*28+7*8+1
=6435

we are looking for x^7, so, which are
component in
(1+x)^7| (1+x)^8 | coefficient
x^7 | 1 | 1
7x^6 | 8x | 56
7C2x^5| 8C2x^2| 7C2 x 8C2
7C3x^4| 8C3x^3| 7C3 x 8C3
7C4x^3| 8C4x^4| 7C4 x 8C4
7C5x^2| 8C5x^5| 7C5 x 8C5
7C6x^1| 8C6x^6| 7C6 x 8C6
7C7=1 | 8C7x^7| 1*8

sum of last column is the answer

we are looking for x^7, so, which are
component in
(1+x)^7| (1+x)^8 | coefficient
x^7 | 1 | 1
7x^6 | 8x | 56
7C2x^5| 8C2x^2| 7C2 x 8C2
7C3x^4| 8C3x^3| 7C3 x 8C3
7C4x^3| 8C4x^4| 7C4 x 8C4
7C5x^2| 8C5x^5| 7C5 x 8C5
7C6x^1| 8C6x^6| 7C6 x 8C6
7C7=1 | 8C7x^7| 1*8

sum of last column is the answer