In: Statistics and Probability
Number of burgers each with k toppings out of 11 are 11Ck
a.
Number of burgers each with 0 toppings = 11C0 = 11! / ((11 - 0)! * 0!) = 1
b.
Number of burgers each with 1 topping1 = 11C1 = 11! / ((11 - 1)! * 1!) = 11! / 10! = 11
c.
Number of burgers each with 2 toppings = 11C2 = 11! / ((11 - 2)! * 2!) = (11 * 10) / 2 = 55
d.
Number of burgers each with 6 toppings = 11C6 = 11! / ((11 - 6)! * 6!) = (11 * 10 * 9 * 8 * 7) / (5 * 4 * 3 * 2 * 1) = 462
e.
Number of burgers each with 8 toppings = 11C8 = 11! / ((11 - 8)! * 8!) = (11 * 10 * 9) / (3 * 2 * 1) = 165
f.
Number of burgers each with 9 toppings = 11C9 = 11! / ((11 - 9)! * 9!) = (11 * 10) / ( 2 * 1) = 55
g.
Number of burgers each with 10 toppings = 11C0 = 11! / ((11 - 10)! * 10!) = 11 / 1 = 11
h.
Number of burgers each with 11 toppings = 11C11 = 11! / ((11 - 11)! * 11!) = 1