Directions: Use your knowledge of statistics and probability to solve the following problems.

1. How many different ways can you make combinations of 2 letters out of the four-letter word LIFE?

2. How many different ways can you make combinations of 7 numbers out of the numbers 1 through 7?

3. How many diagonals can be drawn from each vertex of a hexagon?

4. How many diagonals can be drawn from each vertex of a pentagon?

Answer the following questions about random probabilities. Show all your work, using the combination formula and probability formulas.

5. If there are five different single digits, 1, 2, 3, 4, and 5, then what is the probability that of three numbers, chosen at random, none of them would be 5?

6. Ten different boys are auditioning for a play. The directors are looking to cast only three of the boys. If three of the boys were chosen at random, then what is the probability that all three of the boys chosen are the brothers? Show your answer in fraction and percent, round to the nearest thousandth.

If a card is pulled from a deck of playing cards and a six-sided die is tossed, then what is the probability that the following two independent events will occur?

7. Rolling an odd number and drawing a King.

8. Drawing a 10, and rolling an odd number.

If a dice is rolled and the spinner below with 5 sides, each with the letters A, B, C, D, E is spun, then what is the probability of the following independent events occurring at the same time?