Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2 - 2 matrices- The probability that such formed matrices have all different entries and are non-singular- is-

Total matrices =6^4 Number of matrices with distinct entries nbsp; nbsp; nbsp; nbsp;= 6 × 5 × 4 × 3 = 360 Number of singular matrices with distinct entr ...

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Four dice are...

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Four dice are thrown simultaneously and the numbers shown on these dice are recorded in $2 \times 2$ matrices. The probability that such formed matrices have all different entries and are non-singular, is:

\frac{43}{162}

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\frac{45}{162}

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\frac{22}{81}

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\frac{23}{81}

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Solution

The correct option is A $\frac{43}{162}$
Total matrices $= 6^{4}$
Number of matrices with distinct entries
$= 6 \times 5 \times 4 \times 3 = 360$
Number of singular matrices with distinct entries
i.e. $(1, 2, 3, 6)$ or $(2, 3, 4, 6) = 8 + 8 = 16$
Favourable cases $= 360 - 16 = 344$
Required probability $= \frac{344}{6^{4}} = \frac{43}{162}$

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2 .

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Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2×2 matrices. The probability that such formed matrices have all different entries and are non-singular, is:

The correct option is A 43162Total matrices =64 Number of matrices with distinct entries =6×5×4×3=360 Number of singular matrices with distinct entries i.e. (1,2,3,6) or (2,3,4,6)=8+8=16 Favourable cases =360−16=344 Required probability =34464=43162

Four dice are thrown simultaneously and the numbers shown on these dice are recorded in $2 \times 2$ matrices. The probability that such formed matrices have all different entries and are non-singular, is: