Multiple choice

A card is drawn from a pack. The card is replaced and the pack is reshuffled. If this is done six times, the probability that $2$ herts, $2$ diamonds and $2$ black cards are drawn is

  1. $90.{\left( {\dfrac{1}{4}} \right)^6}$
  2. $\dfrac{{45}}{2}.{\left( {\dfrac{3}{4}} \right)^4}$
  3. $\dfrac{{90}}{{{2^{10}}}}$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is a multinomial distribution problem. Probability of heart = 1/4, diamond = 1/4, black = 1/2. We want 2 of each in 6 trials. P = (6! / (2! 2! 2!)) * (1/4)^2 * (1/4)^2 * (1/2)^2 = 90 * (1/16) * (1/16) * (1/4) = 90 / 1024 = 45 / 512 = 90 / 2^10.

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