Identify which of the following expressions results in an integer.

I. $\frac{15!}{9!}$
II. $\frac{15!}{10!}$
III. $\frac{15!}{8!7!}$

Correct answer marked below

I only

II only

III only

I and II only

I, II, and III

Correct

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Explanation

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Official Explanation

Official

To determine if the expressions yield integers, we evaluate each one.

I.

\frac{15!}{9!} = 15 \times 14 \times 13 \times 12 \times 11 \times 10

, which is an integer.

II.

\frac{15!}{10!} = 15 \times 14 \times 13 \times 12 \times 11

, which is also an integer.…

Comments

SushilApr 23, 2025

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KonradSep 15, 2024

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IsabellaJun 30, 2024

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What this question tests

Your fluency with the order of operations, fractions, decimals, and basic number sense — the foundation every quant question leans on.

Applying the order of operations out of sequence or rounding intermediate values before the final step.