Question

# How many permutations of three items can be selected from a group of six? Use the letters A, B, C, D, E, and F to identify the items, and list each of the permutations of items B, D, and F.

Probability and combinatorics
How many permutations of three items can be selected from a group of six? Use the letters A,
B, C, D, E, and F to identify the items, and list each of the permutations of items B, D, and F.

2021-05-18
Definition permutation (order is important):
$$P_{n,r}=\frac{n!}{(n-r)!}$$
Definition combination (order is not important):
$$C_{n,r}=\frac{n!}{r!(n-r)!}$$
with $$n!=n\cdot(n-1)\cdot...\cdot2\cdot1$$
Given:
$$n=6$$
$$r=3$$
We need to use permutations:
$$P_{6,3}=\frac{6!}{(6-3)!}=\frac{6!}{3!3!}=\frac{6\cdot5\cdot...\cdot1}{3\cdot2\cdot1}=6\cdot5\cdot4=120$$
All ways in which we can select 3 outcomes from the group of three items B,D and F:
BBB, BBD, BDB, DBB, BBF, BFB, FBB, BDF, BFD, DDD, DDB, DBD, BDD, DDF, DFD, FDD, DBF, DFB, FFF, FFB, FBF, BFF, FFD, FDF, DFF, FBD, FDB