MHT CET · Maths · Permutation Combination
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
- A 350
- B 300
- C 200
- D 500
Answer & Solution
Correct Answer
(B) 300
Step-by-step Solution
Detailed explanation
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 \({ }^5 \mathrm{C}_1 \times{ }^5 \mathrm{C}_2=50\)
\(\therefore\) Required number of ways
\(=\) Total number of ways \(-\) Both girls A and B are in the same team
\(=350-50=300\)
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 \({ }^5 \mathrm{C}_1 \times{ }^5 \mathrm{C}_2=50\)
\(\therefore\) Required number of ways
\(=\) Total number of ways \(-\) Both girls A and B are in the same team
\(=350-50=300\)
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