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09 Jun 2026, 16:00
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B
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In how many ways can a group of 8 people be divided into three groups, with 2, 3, and 3 members each?
A. 140
B. 280
C. 420
D. 560
E. 840
A. 140
B. 280
C. 420
D. 560
E. 840
BongBideshini
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09 Jun 2026, 21:44
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Step 1: Form a group of 2
Choose 2 people out of the total 8.
From the remaining 6 people, choose 3.
The remaining 3 people automatically form the last group.
However, the two 3-member groups are identical in size, so each division has been counted twice.
Therefore, the required number of ways = 560 ÷ 2 = 280.
Answer: B
Example:
After choosing the 2-member group, suppose the remaining 6 people are:
A, B, C, D, E, F
If we choose A, B, and C as the first 3-member group, then D, E, F automatically become the second 3-member group.
This gives:
That gives:
Choose 2 people out of the total 8.
- 8C2 = (8 * 7) / (2 * 1) = 28 ways
From the remaining 6 people, choose 3.
- 6C3 = (6 * 5 * 4) / (3 * 2 * 1) = 20 ways
The remaining 3 people automatically form the last group.
- 3C3 = 1 way
However, the two 3-member groups are identical in size, so each division has been counted twice.
Therefore, the required number of ways = 560 ÷ 2 = 280.
Answer: B
Example:
After choosing the 2-member group, suppose the remaining 6 people are:
A, B, C, D, E, F
If we choose A, B, and C as the first 3-member group, then D, E, F automatically become the second 3-member group.
This gives:
- Group of 3: {A, B, C}
- Group of 3: {D, E, F}
That gives:
- Group of 3: {D, E, F}
- Group of 3: {A, B, C}
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