Question

There are 12 different pizza toppings, and Arturo must rank his top 6 in order. How many different possible rankings are there?

Answer 1

12 choices for number 1
11 for #2
10 for #3
9 for #4
8 for #5, and
7 for #6
by the counting principle there are
\[12\times 11\times 10\times 9\times 8\times 7\] ways to rank them

Answer 2

it was that simple?? :) Thank you!!

Answer 3

is another way of doing this with following: P(n,r) n! / (n-r)!

Answer 4

it is the same exactly
that formula you wrote is just a formula, i wouldn't use it

Answer 5

no one want to write
\[\frac{12!}{(12-6)!}=\frac{12!}{6!}\]
\[=\frac{12\times 11\times 10\times 9\times 8\times7\times 6\times 5\times 4\times 3\times 2\times 1}{6\times 5\times 4\times 3\times 2\times 1}\]
\[=12\times 11\times 10\times 9\times 8\times 7\]

Answer 6

the formula just tells you where to stop, don't get married to it, think instead