In a team of 11 players chosen from 9 batsman and 6 bowlers, the number of ways with
8 batsman and 3 bowlers are
аха у х 6 усу аузу
3.
а) 18ө
C) 15
b) 36
d) 540
Answers
Answer:
Given :
There are 6 bowlers and 9 batsman.
The team of 11 should be formed so that it contains at least 4 bowlers.
There are different ways to choose the team members.
We'll use combination formula, since the arrangement of members is not compulsory.
(i) If we are choosing a team where it contains exactly 4 bowlers then it will contain 7 batsman
∴ The number of possible ways =
6
C
4
+
9
C
7
(ii) If we choose a team where 5 bowlers exist then
Number of possible ways =
6
C
5
+
9
C
6
(iii) If we choose a team where there are 6 bowlers then
Number of possible ways =
6
C
6
+
9
C
5
Now, adding all three possibilities will give the total number of ways a team of 11 can be selected, so that it contains at least 4 bowlers.
∴ total number of ways to select a team =
6
C
4
+
9
C
7
+
6
C
5
+
9
C
6
+
6
C
6
+
9
C
5
=
2!4!
6!
+
2!7!
9!
+
1!5!
6!
+
3!6!
9!
+
6!
6!
+
4!5!
9!
=15+36+6+84+1+126
=261
Hence there are total 261 ways.