Question:
Four dice are rolled. The number of possible out comes in which at least one dice shows $2$ is
Four dice are rolled. The number of possible out comes in which at least one dice shows $2$ is
Updated On: Jul 6, 2022
- $1296$
- $671$
- $625$
- none of these
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The Correct Option is B
Solution and Explanation
The total number of possible outcomes is $6^{4}$. The number of possible outcomes in which $2$ does not appear on any dice is $5^{4}$.
$\therefore$ the no. of possible outcomes in which at least one dice shows a $2$ is $6^{4}-5^{4}=1296-625$
$=671$
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Notes on permutations and combinations
Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.