POW #3: Wendy’s Pizza Fiasco

Wendy worried about many things, but the one thing she worried about most was letting down her family with her grades. Not that she ever gave them motive. To the contrary, Wendy probably never received a single grade less than an “A” at any time in her schooling. But that did stop her worrying. She knew better than anyone that her grades were a result of extremely hard work both in school and at home. Nothing came easy to her, like it seemed to for her older brother. He practically sailed through school with a grin and a sparkle in his eye and brought home straight “A” report cards. Somehow in Wendy’s mind, her straight A’s were either elusive or a sham in comparison.
Wendy did not just worry about her grades, though. She worried about practically anything she thought about. Doni, the school jerk, went around chanting “Wendy, Wendy Worry Wart” during recess in the 6th grade to humiliate her. “It worked because it’s true.” she thought. “I am a ridiculous worrier”. If she drank from the water fountain, she would worry either about germs, or contaminants or parasites that she had read about in the science book. So she brought her own bottled water to school, but then started worrying about the leeching plastic poisons she saw on the news. She promptly switched to a metal water bottle. She just could not understand how the other kids could drink the junk they did. But then again, the only thing that did not particularly worry Wendy was what her peers did. Except, that is,  for Tyrone.
Tyrone and Juli were Wendy’s only real friends at school. She had all her classes with Juli (the accelerated ones) and had know her practically all her life. When Tyrone came to their school in the 6th grade they soon became friends with him. Actually, Juli became his friend and Wendy tagged along, since they never really had classes together except for from P.E.. This year all three of them started hanging out at Tyrone’s house after school, working on homework and trying to get Tyrone to understand the bare minimum of Mr. Bott’s math class so he could pass (not an easy task). When Tyrone told them he would be running for Student Council VP, both Wendy and Juli devoted themselves to his campaign. Juli made the posters and Wendy went around school putting them up for him. 
Wendy started to worry about Tyrone. What if he lost? How about Doni, who was going around making fun of Tyrone’s campaign? And what of Juli, who seemed so devoted to Tyrone? Was Wendy out of the picture? She desperately wanted to impress Tyrone, almost more than she wanted to impress her father with A’s in Algebra.
And then Tyrone won! He was now Vice President of the Willowside Student Council and she was his friend. It was as if she herself had won the election, even if she would never have done so on her own.
One of the Student Council’s first act was to buy pizza for all the students who had involved themselves with the election process. They figured that two large pizzas would be enough. It was Tyrone’s responsibility as VP to place the order. The class president told him he should order a pepperoni and onion pizza as well as a green pepper, mushroom and salami pizza. Tyrone forgot to write this down (he never did write down the important stuff), but he was sure he would remember.
Two days later, he told Wendy that he needed help remembering just what specific pizza’s to order. “I never knew that being VP would be this hard, Wendy.” He told her that he was supposed to order a two ingredient and a three ingredient pizzas, but he couldn’t remember what types. He felt embarrassed to go back to the President and tell him he forgot the very first thing he was charged to do. So he begged Wendy for help.
Wendy was desperate to help Tyrone out. She called Pizzarama to find out what types of ingredients they had. Turned out  they only used five ingredients: pepperoni, salami, green pepper, mushroom and onion. “That’s so cheap,” thought Wendy, but it would make her task easier.
“What do we do now, Wendy?” asked Tyrone.
“Well, first I want to figure out how many different two and three ingredient pizzas are even possible at this joint. Then, we can figure out the probabilities you might actually just get it right by ordering random two and three ingredient pizzas. Who knows, maybe we don’t have to worry too much about this.” 

Your Task: Figure out how many possible 2 and 3 ingredient pizzas there are. What is the probability they will get a random order correct? Compare the the possibilities of the two pizzas. What do you notice and why?