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Alice and David are two of the ten people in a group. In how
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14 Aug 2018, 08:15
14 Aug 2018, 08:15
Expert Reply
00:00
Question Stats:
51% (01:42) correct
48% (03:17) wrong based on 29 sessions
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Alice and David are two of the ten people in a group. In how many different ways can this group of 10 people be divided into a group of 7 people and a group of 3 people if Alice and David are to be in the same group?
A. 48
B. 56
C. 64
D. 80
E. 128
Kudos for R.A.E.
A. 48
B. 56
C. 64
D. 80
E. 128
Kudos for R.A.E.
Re: Alice and David are two of the ten people in a group. In how
[#permalink]
14 Aug 2018, 23:15
14 Aug 2018, 23:15
2
Carcass wrote:
Alice and David are two of the ten people in a group. In how many different ways can this group of 10 people be divided into a group of 7 people and a group of 3 people if Alice and David are to be in the same group?
A. 48
B. 56
C. 64
D. 80
E. 128
Kudos for R.A.E.
A. 48
B. 56
C. 64
D. 80
E. 128
Kudos for R.A.E.
Let us consider the first the group of 7,
If DAvid and Alice are in this group then we need to choose only 5 out of 7 from total of 8 people(as David and Alice are considered in the group)
so we have 8C5 = 56 ways.
Now if David and Alice are in the group of 3 people then selecting the group from the total of 8 people will be = 8C1 = 8
So the total no. of ways = 56 + 8 = 64 ways
Intern
Joined: 13 Jul 2018
Posts: 33
Given Kudos: 0
GRE 1: Q159 V151
GPA: 4
WE:Programming (Computer Software)
Re: Alice and David are two of the ten people in a group. In how
[#permalink]
15 Aug 2018, 17:48
15 Aug 2018, 17:48
1
Consider Alice and David as a single person, and then divide the people into groups:
Number of ways = 6(Considering them as one in the group of 7)*3*2 + 7*2(Considering them as one in the group of 3)*2
= 64.
Number of ways = 6(Considering them as one in the group of 7)*3*2 + 7*2(Considering them as one in the group of 3)*2
= 64.
