Given that k and n are positive integers with n greater than k, which expression is equivalent to $k! + (n-k)*(k-1)!$ ?

Answer Choices

Correct answer marked below

k*n!

k! *n

(n-k)!

n*(k+1)!

n*(k-1)!

Correct

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Explanation

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Official Explanation

Official

Let’s consider k = 4 and n = 5. We substitute these values into the expression: k! + (n - k)(k - 1)! = 4! + (5 - 4)(4 - 1)! = 24 + (1)(6) = 24 + 6 = 30. Now we will evaluate the answer choices with n = 5 and k = 4 to see which one equals 30: (A) (k)(n!) = (4)(5!) = (4)(120)…

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Comments

BrianDec 24, 2024

Thank you very much!

ShobithMar 28, 2025

Thank for sharing!

What this question tests

What it tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Common trap

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.

Given that k and n are positive integers with n greater than k, which expression is equivalent to k!+(n−k)∗(k−1)!k! + (n-k)*(k-1)!k!+(n−k)∗(k−1)!?