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In a group of 11 members, 5 have 4 siblings each and 6 have one sibling each. If three members are selected randomly, what is the probability that two of the selected three are siblings?
A. 2/55
B. 8/33
C. 26/55
D. 29/55
E. 25/33
The OA will be automatically revealed on Wednesday 3rd of June 2026 04:45:27 PM Pacific Time Zone
A. 2/55
B. 8/33
C. 26/55
D. 29/55
E. 25/33
The OA will be automatically revealed on Wednesday 3rd of June 2026 04:45:27 PM Pacific Time Zone
02 Jun 2026, 20:25
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Total ways to select 3 members from 11:
11C3 = 165
The 11 members consist of:
Case 1: The sibling pair is chosen from the family of 5.
Number of ways to choose 2 siblings from the 5-member family:
5C2 = 10
The third member must be from outside this family:
6 choices
Favourable ways = 10 × 6 = 60
Case 2: The sibling pair is chosen from one of the three 2-member families.
Choose the sibling pair:
3 ways
Choose the third member from the remaining 9 people:
9 ways
Favourable ways = 3 × 9 = 27
Total favourable ways:
60 + 27 = 87
Required probability:
87/165 = 29/55
Answer: D. 29/55
11C3 = 165
The 11 members consist of:
- One family of 5 siblings.
- Three families of 2 siblings each (6 members total).
Case 1: The sibling pair is chosen from the family of 5.
Number of ways to choose 2 siblings from the 5-member family:
5C2 = 10
The third member must be from outside this family:
6 choices
Favourable ways = 10 × 6 = 60
Case 2: The sibling pair is chosen from one of the three 2-member families.
Choose the sibling pair:
3 ways
Choose the third member from the remaining 9 people:
9 ways
Favourable ways = 3 × 9 = 27
Total favourable ways:
60 + 27 = 87
Required probability:
87/165 = 29/55
Answer: D. 29/55
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02 Jun 2026, 21:26
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There is one family with 5 siblings and three families with 2 siblings each.
Total number of ways to select 3 members from 11 members = 11C3 = 165.
Case 1: The sibling pair comes from the family of 5.
Choose 2 of the 5 siblings: 5C2 = 10.
Choose the third member from the 6 people outside that family: 6 ways.
Number of selections = 10 × 6 = 60.
Case 2: The sibling pair comes from one of the three 2-sibling families.
Choose one of the 3 sibling pairs: 3 ways.
Choose the third member from the remaining 9 people: 9 ways.
Number of selections = 3 × 9 = 27
Total favorable selections = 60 + 27 = 87
Probability = 87/165 = 29/55
Answer: D
Total number of ways to select 3 members from 11 members = 11C3 = 165.
Case 1: The sibling pair comes from the family of 5.
Choose 2 of the 5 siblings: 5C2 = 10.
Choose the third member from the 6 people outside that family: 6 ways.
Number of selections = 10 × 6 = 60.
Case 2: The sibling pair comes from one of the three 2-sibling families.
Choose one of the 3 sibling pairs: 3 ways.
Choose the third member from the remaining 9 people: 9 ways.
Number of selections = 3 × 9 = 27
Total favorable selections = 60 + 27 = 87
Probability = 87/165 = 29/55
Answer: D
