The document discusses a combinatorial problem involving a debate club with 6 girls and 4 boys, requiring the selection of a team of 4 members that includes at most one boy. It outlines the calculations for two cases: selecting 4 girls with no boys and selecting 1 boy with 3 girls, arriving at a total of 380 ways to form the team, with option (a) being the correct answer. Additional details and resources are provided for further learning.

1. Physics Helpline
L K Satapathy
Permutation & Combination 3

2. 10/11/2015
Permutation and Combination 3
Physics Helpline
L K Satapathy
Question : A debate club consists of 6 girls and 4 boys. A team of 4 members is to
be selected from this club including the selection of a captain (from among these 4
members) for the team. If the team has to include at most one boy, then the number
of ways of selecting the team is
(a) 380 (b) 320 (c) 260 (d) 95
Answer :
Given : The team can include at most 1 boy. Hence we have two cases
(i) no boy + 4 girls or (ii) 1 boy + 3 girls
(i) For no boy and 4 girls
6
1 4
6.5.4.34 4 60
1.2.3.4
n C    
4 girls can be selected from 6 girls in ways6
4C
For each of these , the captain can be chosen from 4 members in 4 ways
 For the 1st case

3. 10/11/2015
Permutation and Combination 3
Physics Helpline
L K Satapathy
(ii) For 1 boy and 3 girls
6 4
2 3 1
6.5.44 4 4 320
1.2.3
n C C      
1 boy can be selected from 4 boys in ways4
1C
For each of these , 3 girls can be selected from 6 girls in ways
6
3C
The captain can be chosen from 4 members in 4 ways
 For the 2nd case
1 2 320 60 [ ]380n n nn A s    
 The total number of ways in which the team can be selected is
Correct option = (a)

4. 10/11/2015
Physics Helpline
L K Satapathy
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