Step-by-step explanation:
you do know what a combination stands for ?
n over r = n! / (r! × (n-r)!)
and you know what "!" (factorial) means ?
it means it is the product of
n × (n-1) × (n-2) × (n-3) × ... × 3 × 2 × 1
so, now we only need to calculate the whole thing.
10 over 4 = 10! / (4! × (10-4)!) = 10! / (4! × 6!) =
= 10×9×8×7 / 4×3×2 = 5×3×2×7 = 210
10 over 6 = 10! (6! × (10-6)!) = 10! / (6! × 4!) =
= the same as 10 over 4 = 210
8 over 7 = 8! / (7! × (8-7)!) = 8! / (7! × 1!) = 8
6 over 2 = 6! / (2! × (6-2)!) = 6! /(2! × 4!) =
= 6×5 / 2 = 15
6 over 4 = the same as 6 over 2 = 15
9 over 6 = 9! / (6! × (9-6)!) = 9! / (6! × 3!) =
= 9×8×7 / 3×2 = 3×4×7 = 84
so, we have then
210×210 - 8×15 + 15×84 = 44100 - 120 + 1260 =
= 45240
