In a dance school , there are 14 girls and 15 boys. in how many ways , a group…
2023
In a dance school , there are 14 girls and 15 boys. in how many ways , a group consisting of 3 girls and 7 boys can be formed for a competition ?
- A.
2132840
- B.
2232340
- C.
2132340
- D.
2342340
Attempted by 12 students.
Show answer & explanation
Correct answer: D
Answer: 2342340
Use combinations. Choose 3 girls from 14 and 7 boys from 15. Total number of groups = C(14,3) × C(15,7).
Number of ways to choose 3 girls from 14: C(14,3) = (14 × 13 × 12) / (3 × 2 × 1) = 364.
Number of ways to choose 7 boys from 15: C(15,7) = 6435.
Multiply the two counts: 364 × 6435 = 2,342,340.