Math

QuestionIdentify the correct notation for permutations among these options: rPnr P n, P(n,r)P(n, r), C(n,r)C(n, r), nCr\mathrm{nCr}.

Studdy Solution

STEP 1

Assumptions1. We are looking for the correct representation of permutation. . The options provided are rnr n, (n,r)(n, r), C(n,r)C(n, r), and nCr\mathrm{nCr}.

STEP 2

Permutations refer to the arrangement of items where the order is important. The general formula for permutation is given by(n,r)=n!(nr)!(n, r) = \frac{n!}{(n-r)!}where nn is the total number of items, rr is the number of items to choose, and n!n! denotes the factorial of nn.

STEP 3

Now, let's compare the given options with the general formula for permutation.

STEP 4

The first option rnr n does not match the general formula for permutation. In the general formula, nn comes before rr.

STEP 5

The second option (n,r)(n, r) matches the general formula for permutation. The order of nn and rr is correct, and the notation $$ is commonly used to denote permutations.

STEP 6

The third option C(n,r)C(n, r) does not match the general formula for permutation. The notation CC is commonly used to denote combinations, not permutations.

STEP 7

The fourth option nCr\mathrm{nCr} does not match the general formula for permutation. This notation is also commonly used to denote combinations, not permutations.
Therefore, the correct representation of permutation is (n,r)(n, r).

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