S = {1, 2, 3}

pick two cards out of S, ordering is important.
What are the possible permutations?

(1, 2)
(1, 3)
(2, 1)
(2, 3)
(3, 1)
(3, 2)

6 = 3 * 2 (3 for the first card, 2 for the second card)



X1 = {1, 2, 3}
X2 = {a, b}

X1 x X2 = {(1,a), (1, b), 
           (2,a), (2, b),
           (3,a), (3, b)}
           
           
           
Let p (between 0 and 1) be the probability that a bit is not transmitted correctly. What is the probability that a byte is transmitted with every bit incorrect?

p^8

The permutations of {1, 2, 3, 4} is:

(1, 2, 3, 4)
(1, 2, 4, 3)
(1, 4, 2, 3)
(1, 4, 3 ,2)
(1, 3, 2, 4)
(1, 3, 4, 2)
...
(4, 3, 2, 1)

there are 24 permutations for the set {1,2,3,4}

Permutations of {1, 2, 3, 4}, but we only pick 2 values:

P({1,2,3,4},2) = 
{
(1, 2)
(1, 3)
(1, 4)
(2, 1)
(2, 3)
(2, 4)
(3, 1)
(3, 2)
(3, 4)
(4, 1)
(4, 2)
(4, 3)
}

12 permutations.

C({1,2,3,4},2) =
{
  {1,2},
  {1,3},
  {1,4},
  {2,3},
  {2,4},
  {3,4}
}

6 combinations.