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JEE Main Math Class 12 Probability Part 1 Questions
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© examsnet.com
Question : 48
Total: 100
From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is :
[Online April 9, 2017]
21
220
3
11
1
11
2
23
Validate
Solution:
Probability of 4 member committee which contain atleast one woman.
⇒ P(3M, 1W) + P(2M, 2W) + P(1M, 3W) + P(0M, 4W)
⇒
10
C
3
5
C
1
15
C
4
+
10
C
2
5
C
2
15
C
4
+
10
C
1
5
C
3
15
C
4
+
10
C
0
5
C
4
15
C
4
⇒
600
1365
+
450
1365
+
100
1365
+
5
1365
⇒
1155
1365
∴
Probability of committees to have more women than men.
=
P
(
1
M
,
3
W
)
+
P
(
0
M
,
4
W
)
P
(
3
M
,
1
W
)
+
P
(
2
M
,
2
W
)
+
P
(
1
M
,
3
W
)
+
P
(
0
M
,
4
W
)
=
105
1365
1155
1365
=
1
11
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