Prove algebraically, using factorials, that C(8,4) = C(7,3) + C(7,4)?

Prove algebraically, using factorials, that C(8,4) = C(7,3) + C(7,4)





Prove that C(7,5) = C(4,4) + C(5,1) + C(6,2)

Prove algebraically, using factorials, that C(8,4) = C(7,3) + C(7,4)?
They're both done the same way. Here's the first one:





C(7,3) + C(7,4) =


7! / 3!4! + 7! / 4!3! =


7! / 3!4! + 7! / 3!4! =


2 * 7! / 3!4! =


4 * 2 * 7! / 4 * 3!4!


8 * 7! / 4 * 3!4! =


8 * 7! / 4!4! =


8! / 4!4! =


C(8,4)