math 2: counting

Question 1

general multiplication principle: suppose n choices must be made with m1 ways to make choice 1 and m2 ways to make choice 2, and so on, with mn ways to make choice n. then there are

Answer 1

m1 x m2 x m3 x …..mn different ways to make the entire sequence of choices

Question 2

in general, the number of ways “n” objects can be ordered is

Answer 2

n!

Question 3

in general, there are …. of r objects of n

Answer 3

n!/ (n - r)! permutations

Question 4

in general, the number of ways of choosing r of n objects is …

Answer 4

n!/ (n - r)!r! (combination)

Question 5

special notation for combinations;

Answer 5

nCr = (n/ r) (not actually a fraction), the number of ways r objects can be chosen from n