Q91 / 150 · MHT CET 2024 (09 May Shift 2) · Mathematics

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
  • Correct answer
    B
    300
  • C
    200
  • D
    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 $=350-50=300$

Hence, the correct answer is option: 'B'.

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