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Question
Mathematics
Among the divisors of 504, two are chosen randomly, then the probability that the divisors chosen are even, is
Q. Among the divisors of
504
, two are chosen randomly, then the probability that the divisors chosen are even, is
1945
195
Probability
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A
4
3
B
24
1
C
18
1
D
92
51
Solution:
504
=
2
3
3
2
7
1
∴
Total number of divisors
=
(
3
+
1
)
(
2
+
1
)
(
1
+
1
)
=
4
×
3
×
2
=
24
∴
n
(
S
)
=
24
C
2
Let ‘A’ denote even divisor which are
=
3
(
2
+
1
)
(
1
+
1
)
=
3
×
3
×
2
=
18
∴
n
(
A
)
=
18
C
2
∴
P
(
A
)
=
24
C
2
18
C
2
=
24
18
×
23
17
=
92
51