perform the indicated calculation.

$_{48}p_{2}$

$_{48}p_{2} = \square$ (type a whole number.)

Question

perform the indicated calculation.

$_{48}p_{2}$

$_{48}p_{2} = \square$ (type a whole number.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Combinatorics" ], "new_concepts": [], "current_concepts": [ "Combinatorics", "Permutations vs Combinations" ] } ## Identify the permutation notation Using the *Combinatorics* knowledge point $$ _{n}P_{r} = \frac{n!}{(n-r)!} $$ ## Substitute the given values Using the *Combinatorics* knowledge point $$ \begin{aligned} n &= 48 \ r &= 2 \ _{48}P_{2} &= \frac{48!}{(48-2)!} = \frac{48!}{46!} \end{aligned} $$ ## Simplify the factorial expression Using the *Combinatorics* knowledge point $$ \begin{aligned} _{48}P_{2} &= \frac{48 \times 47 \times 46!}{46!} \ _{48}P_{2} &= 48 \times 47 \end{aligned} $$ ## Calculate the final product Using the *Combinatorics* knowledge point $$ 48 \times 47 = 2256 $$ Perform the indicated calculation. $_{48}P_{2} =$ 2256 (Type a whole number.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Combinatorics" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the permutation notation

Substitute the given values

Simplify the factorial expression

Calculate the final product

Answer: