Question

Involving a product code. Assume that X = {C,D,G) and Y = {6,4,5,7). A code consists of 2 different symbols selected from X followed by 2 not necessarily different symbols from Y How many different codes are possible?

Answer 1

96 different codes are possible.

Explanation:

• First, we have to select two DIFFERENT symbols from X.

This can be done in 3 x 2 = 6 different ways (first we have 3 options and then we have 2 options)

• Secondly we need to select two not necessarily different symbols from Y.

This can be done in 4² = 16 different ways (first we have 4 options and because we can repeat symbols, we have other 4 options for our second choice)

• The total amount of symbols is found by multiplying both numbers since we have to choose 2 symbols from set X AND 2 from set Y

6 x 16 = 96 different codes are possible.