Pizza combinations

Question

If a pizza place has 38 toppings and there is a maximum of six toppings per slice without repeating toppings, how many different combinations of slices are there?

Answer 1

38 choose 6 =

(38*37*36*35*34*33) / (6*5*4*3*2*1) =

38 * 37 * 6 * 35 * 34 * 33 / (5*4*3*2) <---- 6 cancels 36 by factor of 6

38 * 37 * 6 * 7 * 34 * 33 / (4*3*2) <-- 5 cancels 35 by factor of 7

38 * 37 * 6 * 7 * 34 * 11 / (4 * 2) <-- 3 cancels 33 by factor of 11

19 * 37 * 6 * 7 * 34 * 11 / 4 <--- 2 cancels 38

19*37*3 * 7 * 17 * 11 <--- 4 = 2*2 and each two cuts the 6 and 34 in half

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