In a box, there are 6 red balls and 4 blue balls. If 4 boys and 6 girls each randomly pick a ball and keep it, what is the probability that all of the boys choose the same color ball?

Answer Choices

Correct answer marked below

\frac{8}{105}

Correct

\frac{1}{5}

\frac{2}{7}

\frac{4}{55}

\frac{4}{105}

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Explanation

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Official Explanation

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In the box, there are 6 red balls and 4 blue balls. The total number of balls is 10. The boys can either all choose red or all choose blue. The probability that all 4 boys choose red is given by the combination of choosing 4 red balls from 6, divided by the total combinations of choosing 4 balls from 10. This is calculated as [m]…

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Comments

GirirajJan 26, 2025

Greatt

AashrithOct 9, 2024

appreciated!

LangJun 23, 2024

thank you very much!

What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.