Question

Let X ={A,B,C}and Y ={1,2,3,4,5). A product code is formed by selecting two letters - possibly the same - from the set X, and following the letters with two different numbers selected from the set Y. For example, CC52 is allowed. How

many codes are in the sample space? >
A) 225
B)150
C) 120
D) 1680
E) 180"

Answer 1

The total number of codes in the sample space is 180.

Step-by-step explanation:

In this problem, we need to find the number of product codes in the sample space. We are selecting two letters from set X, which contains 3 letters (A, B, C) and two different numbers from set Y, which contains 5 numbers (1, 2, 3, 4, 5).

To find the total number of product codes, we need to multiply the number of choices we have for each part of the code. For the letters, we have 3 choices for the first letter and 3 choices for the second letter (including selecting the same letter). For the numbers, we have 5 choices for the first number and 4 choices for the second number (since the numbers need to be different).

Therefore, the total number of codes in the sample space is 3 * 3 * 5 * 4 = 180.