Question

a new state employee is offered a choice of eight basic health plans, six dental plans, and four vision care plans. how many different health - care plans are there to choose from if one plan is selected from each category? different plans resources ebook submit answer 6. -/1 points details my notes ask your teacher practice another how many three - letter code words can be constructed from the first ten letters of the greek alphabet if no repetitions are allowed? different code words resources ebook

Explanation:

Step1: Apply multiplication principle

Multiply counts of each plan type.
$\text{Total plans} = 8 \times 6 \times 4$

Step2: Calculate the product

Compute the result step by step.
$8 \times 6 = 48$; $48 \times 4 = 192$

Step3: Apply permutation for code words

First letter: 10 choices, second:9, third:8.
$\text{Code words} = 10 \times 9 \times 8$

Step4: Calculate permutation result

Compute the final product.
$10 \times 9 = 90$; $90 \times 8 = 720$

Answer:

1. 192 different plans
2. 720 different code words