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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
John has 5 friends who want to ride in his new car that can accommodat
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24 Feb 2023, 08:31
24 Feb 2023, 08:31
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John has 5 friends who want to ride in his new car that can accommodate only 3 passengers at a time. How many different combinations of 3 passengers can be formed from the 5 friends?
A) 3
B) 8
C) 10
D) 15
E) 20
A) 3
B) 8
C) 10
D) 15
E) 20
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
Re: John has 5 friends who want to ride in his new car that can accommodat
[#permalink]
27 Feb 2023, 02:04
27 Feb 2023, 02:04
1
Expert Reply
This is a combination problem where we want to choose 3 people from a group of 5 friends. We can use the formula for combinations, which is:
n C r = n! / (r!(n-r)!)
where n is the total number of items and r is the number of items we want to choose.
Substituting the values, we get:
5 C 3 = 5! / (3!2!)
= (5 × 4 × 3 × 2 × 1) / [(3 × 2 × 1) × (2 × 1)]
= 10
Therefore, there are 10 different combinations of 3 passengers that can be formed from the 5 friends.
The answer is (C) 10.
n C r = n! / (r!(n-r)!)
where n is the total number of items and r is the number of items we want to choose.
Substituting the values, we get:
5 C 3 = 5! / (3!2!)
= (5 × 4 × 3 × 2 × 1) / [(3 × 2 × 1) × (2 × 1)]
= 10
Therefore, there are 10 different combinations of 3 passengers that can be formed from the 5 friends.
The answer is (C) 10.
gmatclubot
Re: John has 5 friends who want to ride in his new car that can accommodat [#permalink]
27 Feb 2023, 02:04
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