Explain permutations and solve problems involving permutations.

March 29, 2026Mathematics

ScanSolve AI Answer

March 29, 2026

Answer

\frac{n!}{(n-r)!}$.

Here are the solutions to the mathematics questions.

1. Permutations

a) Define permutation. A permutation is an arrangement of objects in a specific order. The order in which the objects are selected or arranged matters.

b) Evaluate: i) $^6P_2$ Step 1: Use the permutation formula $^nP_r = \frac{n!}{(n-r)!}$ . $^6P_2 = \frac{6!}{(6-2)!}$ Step 2: Simplify the factorials. $^6P_2 = \frac{6!}{4!} = \frac{6 \times 5 \times 4!}{4!}$ Step 3: Calculate the result.

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Quick Answer

i) ^6P_2 Step 1: Use the permutation formula ^nP_r = (n!)/((n-r)!). ^6P_2 = (6!)/((6-2)!) Step 2: Simplify the factorials.

Asked on March 29, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on March 29, 2026

Here are the solutions to the mathematics questions. 1. Permutations a) Define permutation. A permutation is an arrangement of objects in a specific order. The order in which the objects are selected or arranged matters. b) Evaluate: i) ^6P_2 Step 1: Use the permutation formula ^nP_r = (n!)/((n-r)!). ^6P_2 = (6!)/((6-2)!) Step 2: Simplify the factorials. ^6P_2 = (6!)/(4!) = (6 × 5 × 4!)/(4!) Step 3: Calculate the result.