8. How many different pizzas can be made with 4 types of crust, 2 types of cheese, and 7 different toppings if each pizza has 1 crust, 1 cheese, and 1 topping?

Problem statement:  The menu at a pizza place lets you pick one of two crust types, one of three sauces, one of five types of cheese, and any number of seven different toppings. How many possible different pizzas can you order that have exactly three different toppings?

Be very careful to read this question critically and to enumerate the number of items correctly:

 "one of two crust types"      2 possibilities

 "one of three sauces"   3 possibilities

 "one of five types of cheese"  5 possibilities

 "any number of seven different toppings"    

      many possibilities (none, any combination of {a,b,c,d,e,f or g})

However, "exactly three different toppings" (not cheeses or sauces) means that you are choosing 3 of 7 toppings (and that's all that this problem asks you).

So, nCr = n! / ((n-r)!r!)        ["n choose r";  n=7; r=3]

    7C3 = 7! / (4!3!)

    7C3 = 5040/144

    7C3 = 35

konichiwa~! my name is zalgo and i am here to answer your anime-related question today. more than likely, kirishima would kill izuku, marry mino and kiss momo. all of this would be my opinion by the way. (and i am also a weeb lol)

i hope this you! : d

stay and stay proud! " - zalgo

(and do you think you can mark me as brainliest? i'd greatly appreciate it! arigato~! )

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this