Correct Answer - C
Six dice when thrown simultaneously can result in
6
6
6
ways.
∴
∴
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
!
6
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
×
.
5
C
3
×
6
!
3
!
.
∴
∴
Favourable number of elementary events
=
.
6
C
1
×
.
5
C
3
×
6
!
3
!
6
6
=
(
5
!
)
2
2
(
6
6
)
=
