Three dice are rolled. The number of possible outcomes in which at lea

1.	Three dice are rolled. The number of possible outcomes in which at least one dice show 4 is 1. 922. 913. 2874. None of these
Answer» Correct Answer - Option 2 : 91 Concept: Required numbers of possible outcomes = Total numbers of possible outcomes – Number of possible outcomes in which 4 does not appear on any dice Calculations: Required numbers of possible outcomes = Total numbers of possible outcomes – Number of possible outcomes in which 4 does not appear on any dice A dice has 6 numbers and since we don't want it to show 4, we are left with five options 1,2,3,5,6. Since any of the numbers can appear on any of the dice, Number of ways in which 4 doesn't appear on any of the dice= 5 × 5 × 5 Hence, the required number of possible outcomes = \(\rm 6^3 - 5^3\) ⇒Hence, the required number of possible outcomes = \(\rm216 - 125 =91\)

Three dice are rolled. The number of possible outcomes in which at least one dice show 4 is 1. 922. 913. 2874. None of these

Answer» Correct Answer - Option 2 : 91

Concept:

Required numbers of possible outcomes = Total numbers of possible outcomes – Number of possible outcomes in which 4 does not appear on any dice

Calculations:

Required numbers of possible outcomes

= Total numbers of possible outcomes – Number of possible outcomes in which 4 does not appear on any dice

A dice has 6 numbers and since we don't want it to show 4, we are left with five options 1,2,3,5,6.

Since any of the numbers can appear on any of the dice,

Number of ways in which 4 doesn't appear on any of the dice= 5 × 5 × 5

Hence, the required number of possible outcomes = \(\rm 6^3 - 5^3\)

⇒Hence, the required number of possible outcomes = \(\rm216 - 125 =91\)

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