Permutations and Combinations - # 2

[Jason]

ex. a

How many two-note permutations can be made with a snare, bass drum, and tom note, without repetition? What is the big idea you see?

\(Combo \,\,1 \)

\(P1: B-T\)

\(P2: T-B\)


\(Combo \,\,2\)

\(P3: T-S\)

\(P4: S-T\)


\(Combo\,\,3\)

\(P5: B-S\)

\(P6: S-B\)

P = 6, You see 6 different unique arrangements (permutations).

\(P(n, r) = \dfrac{n!}{(n - r)!}\)

\(P(3, 2) = \dfrac{3!}{(3 - 2)!} = \dfrac{6}{1} = 6\)

ex. b

How many combinations in ex. a? What is the big idea you see?

\(C(n, r) = \dfrac{n!}{r! (n - r)!}\)

\(C(3, 2) = \dfrac{3!}{2!(3 - 2)!} = \dfrac{6}{2} = 3\)

C = 3, We see 3 different unique groupings. That would be combinations.