JEE Main 2015 · 4 Apr · Shift 1 · Mathematics Q86

← JEE Main 2015 · 4 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 86 of 90

If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is :

\dfrac{55}3\left(\dfrac23\right)^{11}

55\left(\dfrac23\right)^{10}

220\left(\dfrac13\right)^{12}

22\left(\dfrac13\right)^{11}

Answer and worked solution

Official answer: A

The keyed answer treats the balls and boxes as distinguishable (each ball independently in one of 3 boxes). Then the probability that a particular box gets exactly 3 is
$\binom{12}3\left(\frac13\right)^3\left(\frac23\right)^9=\frac{220\cdot2^9}{3^{12}}=\frac{55}3\left(\frac23\right)^{11}.$

Topics:Classical probability Distribution and arrangements

← Previous question Next question →

JEE Main 2015 · 4 Apr · Shift 1, Mathematics question 86