JEE Main 2026 · 6 Apr · Shift 2 · Mathematics Q9

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MathematicsSingle correct+4 / -1Question 9 of 75

A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue and one green ball is :

\dfrac{63}{925}

\dfrac{17}{231}

\dfrac{16}{231}

\dfrac{64}{925}

Answer and worked solution

Official answer: C

Total sequences of pairs. $\dfrac{12!}{2^6}$ .

Favourable. Each pair one blue and one green: order the blues ( $6!$ ) and the greens ( $6!$ ) and pair them off.

Probability.
$\frac{6!\,6!\,2^6}{12!}=\frac{33\,177\,600}{479\,001\,600}=\frac{16}{231}.$

(C)

Topics:Classical probability Combinations

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JEE Main 2026 · 6 Apr · Shift 2, Mathematics question 9