Question

Marissa is doing a Tarot reading in which she must pick 6 cards from a deck of 72. The order of their selection is not important.

Answer 1

This is a combination question or permutation question? I just need whether I can use combination formula or permutation formula with repeated items. Thanks

Answer 2

When order DOES NOT matter that is a combination.
i.e. "a, b, c" is same as "c, a, b" (or same as any order as long as contains the terms.

Example of combinations:
When you choose 10 players for a team, from a class of 20 people. No matter what the order is, in which you choose these people, the team will be the same.
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When order DOES matter that is a permutation.
i.e. "a, b, c" is NOT same as "c, a, b" .

Example of combinations:
When you try to guess a 5-letter password from 8 possible letters.
a d f g h is NOT going to produce the same result as a f d g h

(even the smallest change in order is already a different permutation).

Answer 3

Now, the formulas for calculating combinations and permutations
when you choose \(\color{red}{\rm r}\) number of things, from \(\color{blue}{\rm n}\) number of things: as follows:

\(\large\color{black}{ \displaystyle {\rm Combinations}=\frac{{\rm n}!}{{\rm r!\times (n-r)!}} }\)

\(\large\color{black}{ \displaystyle {\rm Permutations}=\frac{{\rm n}!}{{\rm (n-r)!}} }\)

Answer 4

In math, the left side (in each of the formulas respectively) has a notation of:

\(\large\color{black}{ \displaystyle {\rm nCr}=\frac{{\rm n}!}{{\rm r!\times (n-r)!}} }\)

\(\large\color{black}{ \displaystyle {\rm nPr}=\frac{{\rm n}!}{{\rm (n-r)!}} }\)