Probability questions show up everywhere from introductory statistics to AP Statistics and discrete math courses, and the TI-84 has dedicated tools that make these calculations fast and accurate. Rather than working out factorials by hand or counting outcomes one by one, the calculator can compute combinations, permutations, factorials, and probability distributions in a single keystroke sequence.
Introduction
The TI-84's probability tools live primarily in the MATH menu under the PRB (Probability) submenu, alongside the random number generators found in the same location. These functions are not just conveniences — on timed exams like the SAT Subject Tests, AP Statistics, and college placement exams, being able to compute nCr or nPr instantly can save several minutes per problem compared to manual calculation.
This guide covers the two core counting functions, nCr and nPr, the factorial operator, the random number generators rand and randInt, and the binomial and normal probability distribution functions that most statistics courses require. Each section includes the exact menu path and worked examples so you can check your own calculator against known results.
Combinations with nCr
A combination counts the number of ways to choose a group of items where order does not matter — for example, choosing 3 students from a class of 20 for a committee. Access nCr by typing the total number n, then pressing MATH, arrowing to the PRB submenu, selecting nCr, then typing the number chosen r. The syntax reads as n nCr r on the home screen.
For example, 20 nCr 3 returns 1140, meaning there are 1,140 different three-person committees possible from a group of 20. Combinations appear constantly in probability problems involving cards, lottery numbers, and committee selection, and nCr is almost always faster than expanding the factorial formula n! divided by (r! times (n-r)!) by hand.
Permutations with nPr
A permutation counts arrangements where order matters, such as awarding first, second, and third place among 10 runners. The nPr function sits directly above nCr in the same PRB submenu. The syntax is identical in structure: type n, select nPr, then type r.
For instance, 10 nPr 3 returns 720, representing the number of distinct ways to award three different placements among 10 competitors. A useful way to remember the distinction is that permutations will always return a result greater than or equal to the corresponding combination for the same n and r, since permutations count every reordering as a separate outcome.
Factorials and the ! Function
Factorials underlie both nCr and nPr, and the TI-84 also lets you compute them directly. The factorial symbol is found in the same MATH → PRB menu as option 4. Enter a number, then apply the factorial operator, for example 7! returns 5040.
Factorials grow extremely quickly, and the TI-84 will return an overflow error for numbers larger than about 69 because the result exceeds the calculator's floating-point range. When a problem asks for a ratio of two large factorials, such as 100! divided by 98!, it is often better to simplify algebraically first (in this case to 100 times 99) rather than relying on the calculator to compute each factorial separately.
Random Numbers with rand and randInt
The rand function generates a pseudo-random decimal between 0 and 1, useful for simulating probability experiments such as coin flips or estimating experimental probability through repeated trials. Find it in MATH → PRB → 1:rand. Pressing ENTER repeatedly generates a new value each time.
For whole-number simulations, randInt(lower, upper) generates a random integer within a specified range — randInt(1,6) simulates a single die roll, and randInt(1,6,10) generates ten die rolls at once as a list. These functions are frequently used in AP Statistics simulation-based free-response questions, where you are asked to describe and carry out a simulation design.
Probability Distributions: binompdf and normalcdf
For binomial probability, binompdf(n, p, x) gives the probability of exactly x successes in n independent trials with success probability p, while binomcdf(n, p, x) gives the cumulative probability of x or fewer successes. Both are found under the DISTR menu (2ND, then VARS). For example, binompdf(10, 0.5, 4) gives the probability of exactly 4 heads in 10 fair coin flips.
For continuous distributions, normalcdf(lower, upper, mean, standard deviation) computes the area under a normal curve between two bounds, which corresponds to probability. normalcdf(-1E99, 70, 75, 5) finds the probability of a value falling below 70 in a distribution with mean 75 and standard deviation 5, using -1E99 to represent negative infinity. These two distribution families cover the large majority of probability problems in an introductory statistics course.
Further Reading & Sources