A linguistic club of a certain Institute consists of 6 girls and 4 boys. A team of 4 members to be selected from this group including the selection of a Captain (from among these 4 members) for the team. If the team has to include atmost one boy, the number of ways of selecting the team is

Step-by-step solution

Case I: No boy is included. Selecting 4 girls from 6 girls = ^6 C ₄ Selecting 1 captain from selected members = ^4 C₁ Total number of ways = ^6 C ₄ ^4 C ₁=60 Case II: One boy is included. Selecting 3 girls and 1 boy from given members = ^6 C ₃ ^4 C ₁ . Selecting 1 captain from the selected members = ^4 C ₁ . Total Number of ways = ^6 C ₃ ^4 C ₁ ^4 C ₁=320 . Total Number of ways =320+60=380 .