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📐 Mathematics  ·  Permutations and Combinations  ·  JEE

In how many ways can a team of 3 boys and 2 girls be chosen from 5 boys and 4 girls?

Answer: 5C3 × 4C2 = 60.

  • A 10 × 6 = 60
  • B 5C3 × 4C2 = 60
  • C 120
  • D 5+4=9

Correct answer: B. 5C3 × 4C2 = 60

Explanation: 5C3 × 4C2 = 10 × 6 = 60. Independent choices multiplied together.

StartABCBCACAB6 ordered outcomes (permutations); pairing AB/BA etc gives 3 combinations

Counting tree for selecting 2 items from {A, B, C} without repetition: 3 x 2 = 6 ordered arrangements.

Concept context

Counting, arrangements, and selections

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