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Permutations and combinations
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combinations
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A group consists of 4 girls and 7 boys.
Question
A group consists of
4
girls and
7
boys. In how many ways can a team of
5
members be selected is the team has at least one boy and one girl ?
Hard
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Updated on : 2022-09-05
Solution
Verified by Toppr
Correct option is A)
Total number of girls in the group
=
4
Total number of boys in the group
=
7
Probability of selecting atleast one boy and one girl =?
By considering following ways we can select
i)
1
girls
+
4
boys
⇒
4
C
1
×
7
C
4
ii)
2
girls
+
3
boys
⇒
4
C
2
×
7
C
3
iii)
3
girls
+
2
boys
⇒
4
C
3
×
7
C
2
iv)
4
girls
+
1
boy
⇒
4
C
4
×
7
C
1
Total number of ways
=
(
4
C
1
×
7
C
4
)
+
(
4
C
2
×
7
C
3
)
+
(
4
C
3
×
7
C
2
)
+
(
4
C
4
×
7
C
1
)
=
1
4
0
+
2
1
0
+
8
4
+
7
=
4
4
1
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