Probability with permutations and combinations

The first instance of  is under the Probability and statistics 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 student finds the probability of selecting that particular subgroup.Pcp1.png
 * 2) Coin flip: This problem describes a sequence of coin flips and asks for the probability of a particular outcome. The student finds the probability of that outcome.Pcp2.png

Strategies
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 you 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 you 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) You do need to reduce your fractions in the final answer.