Originally Posted by

**crazy_gal108** **4**. A pizzeria offers 10 different toppings. A group of people plan to order six pizzas, with up to three toppings on each. They decide to order each topping exactly once and to have at least on topping on each pizza. Determine the different cases possible when distributing the toppings in this way and the number of ways that each can be done.

If,

1,2,...10 are the names of the toppings then all the pizza's which can be formed is,

Code:

123
456
789
0XX
XXX
XXX
123
456
78X
90X
XXX
XXX
123
456
7XX
8XX
9XX
0XX
123
45X
67X
89X
0XX
XXX
123
45X
67X
8XX
9XX
0XX
12X
34X
56X
78X
90X
XXX
12X
34X
56X
78X
9XX
0XX

Where X is another topping or nothing (cuz' pizzas can have less then 3 toppings in this problem).