Q: What happens if r is equal to n?

If you choose all items (r = n) without repetition, the number of permutations is simply n! (n factorial), and the combination is exactly 1.

Q: What is the formula for combinations (nCr)?

The combination formula is n! / (r! × (n - r)!), which divides out the redundant orderings found in permutations to leave only unique groupings.

Q: When should I use permutations with repetition?

Use it when items can be reused. Examples include cracking a dial lock, creating a website password, or rolling a die multiple times.

Question 1

What is the difference between Permutations and Combinations?

Accepted Answer

The key difference is purely conceptual: does the 'order' of the items matter? A Permutation is an arrangement of items where the sequence matters (e.g., a combination lock code '123' is different than '321'). A Combination is a selection of items where the sequence doesn't matter (e.g., throwing a fruit salad together consisting of apples and oranges is the same regardless of which you put in the bowl first).

Question 2

What does Replacement (Repetition) mean?

Accepted Answer

When calculating probabilities, 'repetition allowed' means the pool of available total items (n) does not decrease after each pick. For example, rolling a 6-sided die four times allows repetition because rolling a '4' doesn't remove the number '4' from the die on the next roll. Drawing a card from a deck and keeping it out 'without replacement' means the available pool shrinks by 1 each time.

Question 3

What does the exclamation point (!) mean in the formulas?

Accepted Answer

This is the mathematical symbol for Factorial. It means you must multiply a given number by all the strictly positive integers below it. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials grow astronomically fast, which is why permutations of large sets result in massive numbers.

Question 4

Why do some calculators show 'Infinity' or 'NaN' for large permutations?

Accepted Answer

Because factorials grow so rapidly, calculating something like 200! easily exceeds the maximum 64-bit floating-point limit defined by standard computers. Our calculator employs advanced BigInt processing algorithms, allowing you to compute permutations with up to 50,000 baseline items without crashing or prematurely rounding to scientific notation.

Question 5

What is meant by "n" and "r" in formulas?

Accepted Answer

"n" represents the total number of items available to choose from in the entire set, while "r" represents the number of items being selected or arranged.

Question 6

How many ways can I arrange a given word?

Accepted Answer

If all letters are unique (like "CAT"), it is simply n! (3! = 6). If there are repeating letters (like "BOOK"), you divide the total permutations by the factorials of the repeating letter counts.

Question 7

Can permutations be a negative number?

Accepted Answer

No, permutations represent counting physical arrangements or possibilities, so the result must always be a positive whole number or zero (if n < r).

Question 8

What happens if r is equal to n?

Accepted Answer

If you choose all items (r = n) without repetition, the number of permutations is simply n! (n factorial), and the combination is exactly 1.

Question 9

What is the formula for combinations (nCr)?

Accepted Answer

The combination formula is n! / (r! × (n - r)!), which divides out the redundant orderings found in permutations to leave only unique groupings.

Question 10

When should I use permutations with repetition?

Accepted Answer

Use it when items can be reused. Examples include cracking a dial lock, creating a website password, or rolling a die multiple times.

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