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14.Probability
medium
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 $4$ memiers) 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
$95$
(IIT-2016)
Solution
Case $1:$ $0$ boy is included
Selecting $4$ girls from $6$ girls $={ }^6 C _4$
Selecting $1$ captain from the selected members $={ }^4 C _1$
Total for case $1={ }^6 C _4 \times{ }^4 C _1=60$
Case $2:1$ boy is included
Selecting $3$ girls and $1$ boy from given members $={ }^6 C _3 \times{ }^4 C _1$
Selecting $1$ captain from the selected members $={ }^4 C _1$
Total for case $2={ }^6 C _3 \times{ }^4 C _1 \times{ }^4 C _1=320$
Total $=60+320=380$
Standard 11
Mathematics
