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Lesson 111: Solving Problems Involving Permutations — Practice Questions

  1. 1. A club with 10 members needs to elect a president and a vice-president. In how many ways can these two positions be filled? The number of ways is ___.

  2. 2. Which of the following expressions is equivalent to $2^{-4}$?

    • A. -8
    • B. 1/16
    • C. 16
    • D. -16
  3. 3. Calculate the value of the permutation $_7P_3$. The value is ___.

  4. 4. Simplify the expression $10^{-2}$ and write the result as a fraction. The answer is ___.

  5. 5. There are 5 distinct paintings to be arranged on a wall. Which expression represents the total number of possible arrangements?

    • A. $_5P_1$
    • B. $_5P_0$
    • C. $_5P_5$
    • D. $5 \times 4$
  6. 6. A restaurant offers 8 main courses and 6 different side dishes. If a meal consists of one main course and one side dish, how many different meal combinations are possible? The total is ___.

  7. 7. A user is creating a new account password. The password must consist of one letter from the alphabet (26 choices) followed by two digits (10 choices each). How many unique passwords can be created?

    • A. 46
    • B. 260
    • C. 2600
    • D. 286
  8. 8. Simplify the expression by performing the subtraction: $(9x^2 + 2x - 5) - (4x^2 - 7x + 3)$. The result is ___.

  9. 9. Which expression is the result of simplifying $(6y^2 - 3y + 11) + (y^2 + 5y - 4)$?

    • A. $6y^2 + 2y + 7$
    • B. $7y^2 + 2y + 7$
    • C. $7y^2 - 8y + 15$
    • D. $5y^2 - 2y + 7$
  10. 10. When the polynomial $(5m - 9)$ is subtracted from $(12m + 4)$, the result is $7m +$ ___.