A pizza place offers 5 different cheeses and 10 different toppings. In how many ways can a pizza be made with 3 cheese and 6 toppings?

1 Answer
MathFact-orials.blogspot.com
May 28, 2017

2100

Explanation:

We're talking about combinations - that is, we don't care in what order the toppings are chosen (much like we don't care in what order we are dealt a poker hand). The general formula is:

#C_(n,k)=(n!)/((k!)(n-k)!)# with #n="population", k="picks"#

We can calculate the way to pick 3 cheeses from a pool of 5 and we can also calculate the number of ways to pick 6 toppings from a pool of 10. We can then multiply these two numbers to find a total number of ways to do them together.

#C_(5,3)xxC_(10,6)=(5!)/((3!)(5-3)!)xx(10!)/((6!)(10-6)!)=>#

#=>(5xx4xx3!)/(3!xx2)xx(10xx9xx8xx7xx6!)/(6!xx4xx3xx2)#

#=>10xx(10xx9xx8xx7)/24=2100#

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