Solve the equation ^nP3 = 24 ^nC4 for n.

March 30, 2026Mathematics

ScanSolve AI Answer

March 30, 2026

Answer

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

Step 1: Write the formulas for permutations and combinations. The formula for $^nP_r$ is $^nP_r = \frac{n!}{(n-r)!}$ . The formula for $^nC_r$ is $^nC_r = \frac{n!}{r!(n-r)!}$ .

Step 2: Apply the formulas to the given equation. The given equation is $^nP_3 = 24nC_4$ . Substitute the formulas: $\frac{n!}{(n-3)!} = 24 \times \frac{n!}{4!(n-4)!}$

Step 3: Simplify the equation. For the terms to be defined, we must have $n \

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Quick Answer

Write the formulas for permutations and combinations. The formula for ^nP_r is ^nP_r = (n!)/((n-r)!).

Asked on March 30, 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 30, 2026

Step 1: Write the formulas for permutations and combinations. The formula for ^nP_r is ^nP_r = (n!)/((n-r)!). The formula for ^nC_r is ^nC_r = (n!)/(r!(n-r)!). Step 2: Apply the formulas to the given equation. The given equation is ^nP_3 = 24nC_4. Substitute the formulas: (n!)/((n-3)!) = 24 × (n!)/(4!(n-4)!) Step 3: Simplify the equation. For the terms to be defined, we must have $n \