Multiple choice

Three six faced dice are tossed together, then the probability that exactly two of the three numbers are equal is

  1. $165/216$
  2. $177/216$
  3. $51/216$
  4. $90/216$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total outcomes = 6^3 = 216. Outcomes with exactly two equal numbers: (3 * 6 * 5) = 90. The number of ways to choose which two are equal is 3C2=3, the value they take is 6, and the third die can be any of the 5 remaining values.

AI explanation

The total number of outcomes when rolling three six-faced dice is 6 * 6 * 6 = 216. To get exactly two equal numbers, we first choose the matching number in 6 ways, choose the differing number in 5 ways, and select the positions for the matching numbers in 3C2 = 3 ways, giving 6 * 5 * 3 = 90 favorable outcomes. Thus, the required probability is 90/216.

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