Multiple choice

There are 6 identical cubes, with each face coloured differently. What is the probability that each cube will show a different coloured face on top, if thrown simultaneously?

  1. 12/325

  2. 52/325

  3. 5/324

  4. 2/325

  5. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Each cube has 6 faces. Total outcomes for 6 cubes is 6^6. Favorable outcomes where each shows a different face is 6! (permutations of 6 colors). Probability = 6! / 6^6 = 720 / 46656 = 5 / 324.

AI explanation

The total number of possible outcomes when throwing 6 cubes is 6^6, which equals 46656. For each cube to show a different colored face on top, the 6 cubes must show a permutation of the 6 different colors, meaning the first cube has 6 choices, the second has 5, the third has 4, and so on. The number of favorable outcomes is 6 factorial, which equals 720. The probability is 720 divided by 46656, and simplifying this fraction by dividing the numerator and denominator by 144 yields 5/324.

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