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Six dice are thrown simultaneously. The probability that exactly three of them show the same face and ramining three show different faces, isA. `((5!)^(2))/(6^(5))`B. `(5!)/(2!6^(6))`C. `((5!)^(2))/(2(6^(6))`D. `(5!)/(2(6^(6)))` |
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Answer» Correct Answer - C Six dice when thrown simultaneously can result in `6^(6)` ways. `therefore` Total number of elementary events `=6^(6)`. Select a number which occurs on three dice out of six numbers 1,2,3,4,5,6. This can be done in `.^(6)C_(1)` ways. Now, select three numbers out of the remaining 5 numbers. This can be done in `.^(5)C_(3)` ways. Now, we have 6 numbers like 1,2,3,4,4,4, 2,3,6,1,1,1 etc. These digits can be arranged in `(6!)/(3!)` ways. So, the number of ways in which three dice show the same face and the remaining three show distinct faces is `.^(6)C_(1)xx .^(5)C_(3)xx(6!)/(3!)` `therefore` Favourable number of elementary events `= (.^(6)C_(1)xx .^(5)C_(3)xx(6!)/(3!))/(6^(6))=((5!)^(2))/(2(6^(6)))` |
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