Ti 83 C_n Power Series Calculator

This guide explains how to calculate combinations (C_n) using your TI-83 calculator, including the formula, step-by-step instructions, and practical examples. The included online calculator provides an alternative method for those without a TI-83.

What is C_n in Power Series?

In combinatorics, C_n represents the number of combinations of n items taken k at a time. It's calculated using the binomial coefficient formula, which is fundamental in probability, statistics, and discrete mathematics.

Combinations differ from permutations in that order doesn't matter. For example, selecting 2 fruits from an apple and orange is the same as selecting orange and apple - it's just one combination.

Key properties of combinations:

C(n, k) = C(n, n-k)
C(n, 0) = C(n, n) = 1
C(n, 1) = n

How to Use the TI-83 C_n Calculator

Step 1: Access the Math Menu

Press the [2ND] key, then the [MATH] key to access the math functions. Scroll down to find the [PRB] (Probability) menu.

Step 2: Select nCr

In the PRB menu, select option 2: [nCr]. This function calculates combinations.

Step 3: Enter Values

Enter the total number of items (n) followed by the number to choose (k). For example, to calculate C(5,2), enter 5, then 2.

Step 4: View Result

Press [ENTER] to see the result. The TI-83 will display 10, which is the number of ways to choose 2 items from 5.

Tip: The TI-83 can calculate combinations up to n=68. For larger values, use the online calculator below.

The C_n Formula

The combination formula is:

C(n, k) = n! / (k! × (n - k)!)

Where:

n! is the factorial of n
k is the number of items to choose
n must be ≥ k

This formula counts the number of ways to choose k items from n items without regard to order.

Worked Examples

Example 1: Simple Combination

Calculate C(4,2):

C(4, 2) = 4! / (2! × (4-2)!) = 24 / (2 × 2) = 6

There are 6 ways to choose 2 items from 4.

Example 2: Practical Application

In a lottery with 50 numbers, how many ways can you choose 6 numbers?

C(50, 6) = 50! / (6! × 44!) ≈ 15,890,700

There are approximately 15.9 million possible combinations.

Frequently Asked Questions

What's the difference between combinations and permutations?

Combinations count groups where order doesn't matter (like selecting a team), while permutations count arrangements where order matters (like finishing positions in a race).

Can I use the TI-83 for large n values?

The TI-83 can handle n up to 68, but for larger values, use the online calculator which supports much bigger numbers.

Why is C(n, k) equal to C(n, n-k)?

This symmetry comes from the formula - choosing k items from n is the same as leaving out n-k items from n.