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  • When seven dice (each with six faces) are rolled, find the number of outcomes in which at least one die displays 6.   Option: 1</st

When seven dice (each with six faces) are rolled, find the number of outcomes in which at least one die displays 6. 

 

Option: 1

151311 


Option: 2

201811


Option: 3

183411

 


Option: 4

174511


Answers (1)

The dice are rolled 7 times.

The permutation with repetition is given by n^{r}

The total number of possible outcomes is 6^{7}

Thus,

6^{7}=6\times 6\times 6\times 6\times 6\times 6\times 6

6^{7}=279936

The total number of outcomes, when no 6 appears, is  5^{5} 

5^{7}=5\times 5\times 5\times 5\times 5\times 5\times 5

5^{7}=78125

So, the total number of possible outcomes is given by,

6^{7}-5^{7}=279936-78125

6^{7}-5^{7}=201811

Therefore, the number of possible outcomes is 201811.

Posted by

Kshitij

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