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 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Other

Quantitative Aptitude

Probability

Four dice are...

Question

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}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{45}{162}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{22}{81}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{23}{81}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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 $= \frac{344}{6^{4}} = \frac{43}{162}$

Suggest Corrections

Similar questions

Q. Two dice are thrown simultaneously. The probability that the sum of squares of the numbers shown on the dice is a multiple of 2 and 5, is

Q. Three dices are painted with 3 different colours such that the opposite faces of the dice have the same colour. If they are thrown simultaneously, then what is the probability of getting different colours on all the three dices?

Q. Few dice are taken and each die is painted with three different colours such that the opposite faces have the same colour. If three such identical dice are thrown simultaneously, then what is the probability of getting different colours on all the three?

Let

A

be the set of all

3 \times 3

symmetric matrices all whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0.

The number of matrices in

A

such that

| A | = 0

, is

Q. Two dice are thrown at a time. Find the probability that the difference of numbers shown on the dice is

2 .

Join BYJU'S Learning Program

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: