Consider a group of 5 boys and 7 girls. The number of different teams, consisting of 2 boys and 3 girls that…
Consider a group of 5 boys and 7 girls. The number of different teams, consisting of 2 boys and 3 girls that can be formed from this group if there are two specific girls A and B , who refuse to be the members of the same team, is
350
300
200
500
Solution
There are 5 boys and 7 girls in a class.
Total number of ways $={ }^5 \mathrm{C}_2 \times{ }^7 \mathrm{C}_3=350$
If both girls A and B are in the same team, then ${ }^5 \mathrm{C}_1 \times{ }^5 \mathrm{C}_2=50$
$\therefore \quad$ Required number of ways
$=$ Total number of ways
- Both girls A and B are in the same team
$=350-50=300$