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10 Feb 2021, 07:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
37% (03:30) correct
63%
(02:36)
wrong
based on 49
sessions
History
Date
Time
Result
Not Attempted Yet
An English school and a Vernacular school are both under one superintendent. Suppose that the superintendentship, the four teachership of English and Vernacular school each, are vacant, if there be altogether 11 candidates for the appointments, 3 of whom apply exclusively for the superintendentship and 2 exclusively for the appointment in the English school, the number of ways in which the different appointment can be disposed of is :
(A) 268
(B) 1080
(C) 4320
(D) 6320
(E) 25920
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
(A) 268
(B) 1080
(C) 4320
(D) 6320
(E) 25920
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
22 Feb 2021, 14:02
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Bunuel
We are filling in for 9 positions, one superintendent, 4 teacherships of each school. The superintendent has only 3 options. The Vernacular teachership is filled in by selecting any 4 from the rest of the candidates (11 - 3 - 2 = 6 people). Then we can note the rest of the 4 candidates will go towards the English school, so 6C4 options only for those 8 applicants.
So we should have 3*(6C4) groups but we are asking how the appointments can be arranged. Each school has 4 slots so that is an extra 4! to multiply for each school. Therefore the answer is \(3*(6C4)*4! * 4! = 3*(6C2) * 24 * 24 = 45 * 24 * 24 \approx 1000*24\) and the only close answer is E.
Ans: E
13 Mar 2024, 05:58
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TestPrepUnlimited
This question is poorly worded.
"Disposed of" is ambiguous at best.
There is nothing in the question that distinguishes the positions in the two schools beyond their overall missions of teaching English and Vernacular.
If the question had said "positions in each of four grade levels" then there would be a basis for the distinction.
So there is no basis for arranging the positions within each school at 4!*4!, reducing the answer to:
3*6!/4!2 = 45
As identified in the quoted response
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