saswata4s wrote:
Three dice (each having six faces with each face having one number from 1 to 6) are rolled. What is the number of possible outcomes such that at least one dice shows the number 2?
(A) 36
(B) 81
(C) 91
(D) 112
(E) 116
We need to determine, when rolling three dice, the number of outcomes in which at least one die shows a 2.
We should first recall the following formula:
Total number of ways to roll 3 dice = number of ways with at least one 2 + number of ways with no 2s.
Since there are 6 x 6 x 6 = 216 possible outcomes when rolling 3 dice, we have:
216 = number of ways with at least one 2 + number of ways with no 2s
number of ways with at least one 2 = 216 - number of ways with no 2s
There are 5 x 5 x 5 = 125 outcomes in which no 2 is shown.
Thus, there are 216 - 125 = 91 outcomes in which at least one 2 is shown.
Answer: C
_________________