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14 Jul 2020, 14:48
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
60% (03:04) correct
40%
(01:36)
wrong
based on 10
sessions
History
Date
Time
Result
Not Attempted Yet
A school has vacancy for a librarian, a Physics teacher, and four Computer teachers. There are 3 candidates for the position of Librarian, 2 candidates for the position of Physics teacher, and 7 candidates for the position of computer teachers. If 2 out of 7 computer teachers refuse to be on the same team, how many different ways are there to fill the vacancies are possible?
- 35
- 150
- 210
- 60
- 70
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14 Jul 2020, 16:24
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Kav24
For the librarian there are 3 options, for the physics teacher there are 2 options. The key part is the number of viable arrangement for 4 computer teachers.
Typically we would find 7C4 = 7C3 = 7 * 6 * 5 / (3!) = 35 combinations, yet there are 2 teachers that do not want to be in the same group. We may count how many groups have those 2 teachers and subtract that number from 35 to find the number of desired groups for computer teachers.
We need to form a group of 4, two spots are filled in with the two teachers mentioned above, and the other 2 spots must be filled in from the rest of the 5 computer teachers. Therefore there are 5C2 groups out of the 7C4 groups we cannot take.
Out of the 7C4 = 35 combinations, we must remove 5C2 = 5 * 4 / 2! = 10 options that represent the case where these two teachers are grouped. Therefore 35 - 10 = 25 groups are available for computer teachers.
Finally 3 * 2 * 25 = 150 would be the answer.
Ans: B
14 Jul 2020, 18:50
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Kav24
Ways to select librarian =3C1
Ways to select physics teacher =2C1
Ways to select computer teacher=7C4
But, as the question mentioned 2 out of those 7 candidates for position of computer teacher are refuse to be on the same team
Lets calculate the number of ways if the 2 candidates want always to be on the same team
Let the 7 candidate be
A,B,C,D,E,F,G
And among those let A,B decided to be on same team
Team of 4 two already filled A,B rest 2 spot fill by 5C2 ways
3C1*2C1*(7C4-5C2)=150 ways
Posted from my mobile device
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
