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MM1D1a

MM1D1a. Counting Techniques. Multiplication Principle of Counting. If a task consists of a sequence of choices in which there are p selections for the first choice, q selections for the second choice, r selections for the third choice, and so on.

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MM1D1a

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  1. MM1D1a Counting Techniques

  2. Multiplication Principle of Counting If a task consists of a sequence of choices in which there are p selections for the first choice, q selections for the second choice, r selections for the third choice, and so on. Then the task of making these selections can be done in the following number of different ways.

  3. If a license plate consists of a letter, then 5 numbers, how many different types of license plates are possible?

  4. If a license plate consists of a letter, then 5 numbers, how many different types of license plates are possible?

  5. Suppose that you have 5 different trees that you wish to plant. In how many different ways can the 5 trees be planted in a row?

  6. A permutation is an ordered arrangement of n distinct objects without repetitions. The symbol nPr represents the number of permutations of n distinct objects, taken r at a time,where r<n.

  7. Determine the value of 9P3.

  8. Suppose a committee consists of 10 people. In how many ways can the chair and vice-chair of the committee be chosen if the first person randomly selected is the chair and the second person randomly selected is the vice-chair.

  9. A combination is an arrangement, without regard to order, of n distinct objects without repetitions. The symbol nCr represents the number of combinations of n distinct objects taken r at a time, where r<n.

  10. Determine the value of 9C3.

  11. The United States Senate consists of 100 members. In how many ways can 4 members be randomly selected to attend a luncheon at the White House?

  12. A landscape architect has 3 Sugar Maples, 2 Weeping Willows, and 4 Green Ash trees to plant along a street in a new subdivision. In how many different ways can the trees be planted?

  13. What is the probability of obtaining 3 of a kind when 5 cards are drawn from a standard 52-card deck?

  14. What is the probability of obtaining 3 of a kind when 5 cards are drawn from a standard 52-card deck? P(3 of a kind) = 0.0211

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