Probability with permutations and combinations
Probability with perm comb 256
Exercise Name: Probability with permutations and combinations
Math Missions: High school statistics and probability Math Mission, Precalculus Math Mission, Mathematics III Math Mission
Types of Problems: 2

The Probability with permutations and combinations exercise appears under the High school statistics and probability Math Mission, Precalculus Math Mission and Mathematics III Math Mission. This exercise uses the concepts of combinations and permutations in order to calculate probabilities.

Types of Problems

There are two types of problems in this exercise:

  1. Selecting a group: This problem describes a group of boys and girls from which a subgroup is to be selected. The user finds the probability of selecting that particular subgroup.

    Selecting a group

  2. Coin flip: This problem describes a sequence of coin flips and asks for the probability of a particular outcome. The user finds the probability of that outcome.

    Coin flip


This exercise is medium to get accuracy badges because although there are only two types of problems, they are intensive. Speed badges should be considered medium and almost easier than accuracy badges as soon as user master the two types of problems described above.

  1. On the Selecting a group problem the probability can always be found as a combination over a combination. If user know how to use a calculator to find combinations this makes the problem very fast.
  2. On the Coin flip problem the answer is always a combination over a power of two. Again, with combinations in the calculator this problem can be done quickly.
  3. users do need to reduce the fractions in the final answer.

Real-life Applications

  1. Probability, along with decimals, percents, and fractions are used to determine the probability of a basketball player making a shot.
  2. Data and statistics appear in news reports and in the media every day.
  3. Many of the problems in this exercise could be viewed as real-life applications.
  4. Statistics can be seen more frequently than calculus in every day life.

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