Permutation, Combination, Independent, and Dependent

What does ₁₀P₅ mean?

• Permutations with 5 choices and 10 positions

• Permutations with 10 choices and 5 positions

• Permutations with 5 numbers and 10 operations

• Permutations with 5 hot dogs and 10 drinks

Which of the following is an example of combination?

• Form a passcode with 4 digits

• Students line up in a queue to assembly

• Choose 4 students in a class committee

• Choose the chairperson, secretary and treasurer in a club

Choosing 3 toppings for your sundae out of a list of 15.

• Combination

• Permutation

• Factorial

• Neither

Calculate ₁₁C_{5 .}

The outcome of one event does not affect the outcome of the other event.

• independent event

• dependent event

Pablo chooses a colored marble from a mixed bag and writes down the color. Pablo leaves it out and then draws another.

• Independent

• Dependent

A bag contains some red-colored and some blue-colored marbles. First a red-colored marble is drawn and then, without replacing the first marble, a blue-colored marble is drawn. Are the two events independent or dependent?

answer choices

• Independent

• Dependent

Determine whether the question would be a permutation or combination: Five students from 90 will be selected to count ballots for the Class President election. How many groups of 5 students could be selected to count ballots?

• Permutation

• Combination

• Neither

Answer explanation

The question involves selecting a group of students from a larger set, which aligns with the concept of combinations, not permutations. Therefore, the correct choice is Combination.

What does ₁₀P₅ mean?

• Permutations with 5 choices and 10 positions

• Permutations with 10 choices and 5 positions

• Permutations with 5 numbers and 10 operations

• Permutations with 5 hot dogs and 10 drinks

Determine whether the following scenarios are a permutation or a combination:
 
Selecting a lead and an understudy for a school play.

• Combination

• Permutation

Answer explanation

Selecting a lead and an understudy involves arranging two distinct roles, making it a permutation as order matters in this scenario.