Correct Answer - C
We have,
Probability of getting a heart in a draw
=
13
52
=
1
4
Probability of getting a diamond in a draw
=
13
52
=
1
4
Probability of getting a black card in a draw
=
26
52
=
1
2
In 6 draws, 2 draws must contain hearts, 2 draws must contain diamond cards and 2 draws must contain black cards. This can happen in
.
6
C
2
×
.
4
C
2
×
.
C
_
2
mutually exculusive ways and the probability of each such way is
(
1
4
)
2
×
(
1
4
)
2
×
(
1
4
)
2
Hence, required probability
=
.
6
C
2
×
.
4
C
2
×
(
1
4
)
2
×
(
1
4
)
2
×
(
1
2
)
2
=
90
×
(
1
2
)
10
