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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
A firm has 4 senior partners and 6 junior partners. How many different
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15 Dec 2022, 07:58
15 Dec 2022, 07:58
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Question Stats:
66% (01:47) correct
33% (03:43) wrong based on 3 sessions
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A firm has 4 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner. (Two groups are considered different if at least one group member is different)
A. 48
B. 100
C. 120
D. 288
E. 600
A. 48
B. 100
C. 120
D. 288
E. 600
Re: A firm has 4 senior partners and 6 junior partners. How many different
[#permalink]
16 Dec 2022, 23:40
16 Dec 2022, 23:40
Expert Reply
Total # of different groups of 3 out of 10 people: \(C^3_{10}=120\);
# of groups with only junior partners (so with zero senior memeber): \(C^3_6=20\);
So the # of groups with at least one senior partner is {all} - {none} = {at least one} = 120 - 20 = 100.
Answer: B.
# of groups with only junior partners (so with zero senior memeber): \(C^3_6=20\);
So the # of groups with at least one senior partner is {all} - {none} = {at least one} = 120 - 20 = 100.
Answer: B.
gmatclubot
Re: A firm has 4 senior partners and 6 junior partners. How many different [#permalink]
16 Dec 2022, 23:40
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