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n00bpron00bpron00b
Students
 
Posts: 89
Joined: Sun Apr 20, 2014 6:12 pm
 

Q) 6 Permutation | Combination Word Problem Book

by n00bpron00bpron00b Sun Jan 04, 2015 6:10 am

Hi Tommy,

Wish you a very happy new year :)

2 Types of Crust : Deep Dish, Thin Crust

5 types of toppings
-> Tomatoes
-> Sausage
-> Peppers
-> Onions
-> Pepperoni

2 Types of Pizza's
-> extra cheese
-> regular

In the answer grid, why has the author used combinations to select 4 toppings from a basket of 5 total toppings.

Selecting Tomatoes, Sausage, Peppers, Onions is different from selecting Pepperoni,Tomatoes,Sausage,Peppers (the output in each case is different right ?)

This is what I did

Types of crust can be selected in 2 ways
Types of pizza can be selected in 2 ways
And 4 toppings 2 x 2 x 2 x 2 (Using FCP)

Total : 64 ways

Please let me know.

Thanks :)
tommywallach
Manhattan Prep Staff
 
Posts: 1917
Joined: Thu Mar 31, 2011 11:18 am
 

Re: Q) 6 Permutation | Combination Word Problem Book

by tommywallach Tue Jan 06, 2015 5:37 pm

Hey Noob,

I'm not sure I understand your question. The question itself stipulates that they are only choosing 4 toppings. So I'm not sure why you're placing 2s, given that there are 5 choices. The correct way to represent that would be:

5 * 4 * 3 * 2 / 4! (that's 4 toppings, with five choices for the first topping, 4 choices for the next topping, 3 choices for the next topping, and 2 choices for the final topping -- then we divide by the # of slots factorial wherever order doesn't matter. Topping order doesn't matter, so we'll divide by 4!)

-t