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Question

A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including a selection of a captain (from among these four 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
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B
320
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C
260
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D
95
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Solution

The correct option is A 380
Case 1 : 0 boy is included
Selecting 4 girls from 6 girls =6C4
Selecting 1 captain from the selected members =4C1

Total for case 1 =6C4×4C1=60

Case 2 : 1 boy is included
Selecting 3 girls and 1 boy from given members =6C3×4C1
Selecting 1 captain from the selected members =4C1

Total for case 2 =6C3×4C1×4C1=320

Total =60+320=380

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