Math Problem Statement

Simplify the expression (11P5) / (11^5).

Solution

The image shows the mathematical expression:

11P5115\frac{^{11}P_5}{11^5}

This expression involves two parts:

  1. 11P5^{11}P_5: This represents the number of permutations of 5 items selected from 11. The formula for permutations is:

nPr=n!(nr)!^{n}P_r = \frac{n!}{(n - r)!}

For 11P5^{11}P_5, it would be:

11P5=11!(115)!=11!6!^{11}P_5 = \frac{11!}{(11 - 5)!} = \frac{11!}{6!}

  1. 11511^5: This is the exponentiation of 11 raised to the power of 5.

To simplify the expression, we need to calculate both parts and then divide the permutation result by 11511^5.

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Math Problem Analysis

Mathematical Concepts

Permutations
Exponentiation
Factorials

Formulas

nPr = n! / (n - r)!
Exponentiation: a^b

Theorems

Fundamental Principle of Counting

Suitable Grade Level

Grades 10-12