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How to Put Ncr in Calculator Ti 84

Reviewed by Calculator Editorial Team

Calculating combinations (nCr) on your TI-84 calculator is straightforward once you know the correct sequence of steps. This guide will walk you through the process, explain the formula, and provide troubleshooting tips.

What is nCr?

nCr (also written as C(n,r) or "n choose r") represents the number of ways to choose r items from a set of n items without regard to order. The formula for combinations is:

nCr = n! / (r! × (n - r)!)

Where:

  • n! (n factorial) is the product of all positive integers up to n
  • r is the number of items to choose
  • n must be greater than or equal to r

Combinations are used in probability, statistics, and many real-world applications where order doesn't matter.

Calculator Setup

Before you begin, ensure your TI-84 is in the correct mode:

  1. Press the MODE button
  2. Ensure the calculator is in "Math" mode (not "Base" or "Stat")
  3. Check that the "Decimal" setting is appropriate for your needs

Note: The TI-84 Plus and TI-84 Plus C Silver Edition both support combination calculations.

Step-by-Step Instructions

Method 1: Using the nCr Function

  1. Press the MATH key
  2. Use the arrow keys to highlight PRB (Probability)
  3. Select nCr (option 2)
  4. Enter the value for n (total items)
  5. Press the comma (,) key
  6. Enter the value for r (items to choose)
  7. Press ENTER to see the result

Method 2: Using the Factorial Function

  1. Press the MATH key
  2. Select PRB (Probability)
  3. Choose ! (Factorial, option 1)
  4. Enter the value for n, press ENTER
  5. Repeat for r and (n-r)
  6. Store these values in memory (STO button)
  7. Use the division function to calculate n! / (r! × (n-r)!)

Tip: For large values of n and r, the calculator may display an error if the result is too large for its display. In this case, use scientific notation or consider using a different calculator.

Worked Example

Let's calculate how many ways you can choose 3 cards from a standard deck of 52 playing cards (order doesn't matter).

  1. Press MATH → PRB → nCr
  2. Enter 52, press comma, enter 3
  3. Press ENTER
  4. The calculator displays 22100

This means there are 22,100 different possible 3-card combinations from a 52-card deck.

Troubleshooting

Common Issues and Solutions

  • Error: INVALID DIM - This occurs when r is greater than n. Make sure n is larger than r.
  • Error: OVERFLOW - The result is too large for the calculator. Try using scientific notation or a different calculator.
  • Calculator not responding - Reset the calculator by pressing the ON button again.

If you're still having trouble, check that your calculator is not in a locked state (press ALPHA + 0 to unlock if needed).

FAQ

Can I calculate permutations on the TI-84?

Yes, permutations (nPr) are calculated similarly to combinations but use the nPr function in the PRB menu.

What's the difference between nCr and nPr?

Combinations (nCr) count groups where order doesn't matter, while permutations (nPr) count arrangements where order does matter.

How do I clear the calculator screen?

Press the CLEAR button to reset the calculator display.