Math

QuestionIdentify the correct notation for permutation from these options: rPn\mathrm{rPn}, P(n,r)P(n, r), C(n,r)C(n, r), nCr\mathrm{nCr}.

Studdy Solution

STEP 1

Assumptions1. The problem is asking for the correct representation of permutation. . Permutation is a way to arrange 'r' items out of 'n' items, where order matters.
3. The four options given are rn\mathrm{rn}, (n,r)(n, r), C(n,r)C(n, r), and nCr\mathrm{nCr}.

STEP 2

Let's analyze each option one by one.
The first option is rn\mathrm{rn}. In the context of permutations, '' usually stands for permutation. However, the order of 'r' and 'n' is incorrect. In permutations, 'n' is the total number of items and 'r' is the number of items to select, so 'n' should come before 'r'. Therefore, rn\mathrm{rn} is not a correct representation of permutation.

STEP 3

The second option is (n,r)(n, r). This is a common notation for permutation, where 'n' is the total number of items and 'r' is the number of items to select. The order of 'n' and 'r' is correct. Therefore, (n,r)(n, r) is a correct representation of permutation.

STEP 4

The third option is C(n,r)C(n, r). In the context of combinatorics, 'C' usually stands for combination. In combinations, order does not matter, which is different from permutations where order does matter. Therefore, C(n,r)C(n, r) is not a correct representation of permutation.

STEP 5

The fourth option is nCr\mathrm{nCr}. This is a common notation for combination, not permutation. Therefore, nCr\mathrm{nCr} is not a correct representation of permutation.

STEP 6

Based on the analysis of all four options, the correct representation of permutation is (n,r)(n, r).
The solution is (n,r)(n, r).

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