Probability problems often use factorials, combinations, permutations and distribution functions. The calculator can speed up computation, but you still need to identify the correct model.
Factorials
Factorials count ordered arrangements and appear in many probability formulas. A factorial grows quickly, so calculators are useful for large values.
Make sure the input is a nonnegative whole number when using factorial.
Combinations
Combinations count selections where order does not matter. They are used in binomial probability, choosing groups and many counting problems.
Look for words like choose, select or committee when deciding whether combinations apply.
Permutations
Permutations count arrangements where order matters. They are used when first, second and third positions are different outcomes.
If changing the order changes the result, it is usually a permutation problem.
Binomial probability
Binomial settings involve a fixed number of trials, two outcomes, constant probability and independent trials.
Use binomial tools only when those assumptions are reasonable. Otherwise, the calculation may be fast but conceptually wrong.
Normal probability
Normal distribution tools require mean, standard deviation and boundary values. Sketching the distribution helps avoid entering the wrong lower or upper bound.
Check whether the problem asks for less than, greater than, between or outside an interval.
Quick reference table
| Tool | Use when |
|---|---|
| n! | Counting arrangements of n items |
| nCr | Selecting without order |
| nPr | Arranging with order |
| binompdf | Exact binomial probability |
| binomcdf | Cumulative binomial probability |
| normalcdf | Area under a normal curve |