Multiple choice

Four dice (six faced ) are rolled. The number of possible outcomes in which at least one dies shows $2$ is

  1. $1296$
  2. $625$
  3. $671$
  4. $None\ of\ these$
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C Correct answer
Explanation

There are 6^4 = 1296 total outcomes. Outcomes with no die showing 2 are 5^4 = 625, so outcomes with at least one 2 are 1296 - 625 = 671.

AI explanation

The total number of possible outcomes when rolling four six-faced dice is 6^4, which equals 1296. To find the outcomes where at least one die shows 2, we use the method of complementary counting by finding the outcomes where no die shows 2. The number of outcomes where no die shows 2 is 5^4, which equals 625. Subtracting the complementary outcomes from the total gives 1296 minus 625. The result is 671.

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