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In how many ways can 10 students be divided into three groups, one group of 4 students and two groups of 3 students each?
- 10! / (4! * 3! * 3!)
- 2100
- 10C4 * 5C3
- 10! / (6! * 3! * 3!) * (1/2)
Correct answer: 2100
Solution
Choose 4 from 10 in C(10,4)=210 ways, then divide the remaining 6 into two groups of 3: C(6,3)/2!=10 ways (dividing by 2! since the groups of 3 are unlabeled). Total = 210*10 = 2100.
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