Berikut ini adalah pertanyaan dari fabian84 pada mata pelajaran Ujian Nasional untuk jenjang Sekolah Menengah Atas
B) Either Fred or Kate must participate, but both of them cannot participate at the same time
C) Fred can only participate if Willy will participate
D) Jak cannot participate unless Homer participates
If the manager realizes that Kate will not be able to participate, how many different 4-member groups can be made, given the above considerations?
Select one:
a.
2
b.
3
c.
4
d.
5
Jawaban dan Penjelasan
Berikut ini adalah pilihan jawaban terbaik dari pertanyaan diatas.
Jawaban:
To solve this problem, we can use a combination of logic and counting principles. We know that there are 7 members in the dance group, but we need to consider the given conditions for selecting the 4-member groups. Let's analyze each condition and see how it affects the number of possible groups.
A) Only one can participate between Homer and Gavin
This means that we can only choose either Homer or Gavin, but not both. So we have 2 options for this slot.
B) Either Fred or Kate must participate, but both of them cannot participate at the same time
This means that we can choose either Fred or Kate, but not both. So we have 2 options for this slot.
C) Fred can only participate if Willy will participate
This means that if we choose Fred, then we must also choose Willy. So we have 1 option for this slot.
D) Jak cannot participate unless Homer participates
This means that if we do not choose Homer, then we cannot choose Jak. So we have 1 option for this slot if we choose Homer, and 0 options if we choose Gavin.
Now let's put everything together. If Kate cannot participate, then we have 6 members to choose from, but we must also consider the conditions. Here are the possible cases:
Case 1: We choose Homer
- We have 2 options for the Homer/Gavin slot
- We have 2 options for the Fred/Kate slot (we cannot choose Kate, so we must choose Fred and Willy)
- We have 1 option for the Willy/Fred slot (we must choose Willy if we choose Fred)
- We have 3 options for the remaining slot (Bruno, Jak, and either Gavin or Kate)
Total number of groups: 2 x 2 x 1 x 3 = 12
Case 2: We choose Gavin
- We have 1 option for the Homer/Gavin slot (we cannot choose Homer)
- We have 2 options for the Fred/Kate slot (we cannot choose Kate, so we must choose Fred and Willy)
- We have 1 option for the Willy/Fred slot (we must choose Willy if we choose Fred)
- We have 3 options for the remaining slot (Bruno, Jak, and either Homer or Kate)
Total number of groups: 1 x 2 x 1 x 3 = 6
Therefore, the total number of different 4-member groups that can be made is 12 + 6 = 18. Answer: There are 18 different 4-member groups that can be made.
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Last Update: Wed, 26 Jul 23