Questions

MATH Integrated Math III - Unit 33: Probability: Fundamental Counting Principle, Permutations, Combinations

1) How are theoretical and experimental probabilities similar? How are they different?

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Use the following scenario to solve the next three problems: A bag contains 4 white cards, 3 black cards, and 6 green cards. Find the probability of each event for one draw.

2) a white card

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3) a black card

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4) a green card

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For the next four problems, calculate the probability of each event for one roll of a die.

5) an even number

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6) a number less than 3

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7) a number greater than 6

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8) a number less than 6

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Use the Fundamental Counting Principle to find the number of possible passwords (with no letters or digits excluded) for the conditions in the next two problems.

9) 2 digits followed by 3 letters followed by 1 digit

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10) 2 letters followed by 4 digits

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Permutations

11) Evaluate the expression.

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12) Evaluate the expression.

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13) Evaluate the expression.

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14) Evaluate the expression.

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15) Evaluate the expression.

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For the next five problems, find the number of permutations of the first 8 letters of the alphabet for each situation.

16) taking 5 letters at a time

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17) taking 1 letter at a time

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18) taking all 8 letters at a time

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19) taking 3 letters at a time

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20) taking 4 letters at a time

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Combinations

21) Find the value of the expression.

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22) Find the value of the expression.

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23) Find the value of the expression.

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24) Find the value of the expression.

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Find the number of ways each committee can be selected in the next two problems.

25) 3 people from a group of 5

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26) 8 people from a group of 12

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27) How many different 12-member teams can be chosen from a pool of 32 people?

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28) A test consists of 20 questions and students are to answer 16 of them. In how many different ways are the students able to choose the 16 questions?

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Permutations and Combinations

For the next four problems, determine whether each situation involves a permutation or a combination.

29) selecting four articles for publication when 302 articles (equal in quality) were submitted

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30) awarding four out of 200 contestants prizes of $200, $150, $100, and $50 (all contestants performed equally well)

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31) selecting nine players from a team of 22 (all equally talented) to start the baseball game

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32) selecting a secretary and treasurer from a class of 210 students (all students equally qualified for the positions)

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