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There are 3 doors to a lecture room. In how many ways can a
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07 May 2019, 10:06
07 May 2019, 10:06
Expert Reply
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Question Stats:
63% (00:23) correct
36% (00:11) wrong based on 19 sessions
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There are 3 doors to a lecture room. In how many ways can a lecturer enter and leave the room?
(A) 1
(B) 3
(C) 6
(D) 9
(E) 12
(A) 1
(B) 3
(C) 6
(D) 9
(E) 12
Re: There are 3 doors to a lecture room. In how many ways can a
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09 May 2019, 00:34
09 May 2019, 00:34
Shouldn't it be 3c1?
Re: There are 3 doors to a lecture room. In how many ways can a
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10 May 2019, 02:55
10 May 2019, 02:55
Expert Reply
Here, order is important. Suppose A, B, and C are the three doors.
The lecturer can enter and exit through the same door, repetition is allowed.
Doors are different. They are not indistinguishable, so no indistinguishable objects. Hence, we have a permutation problem, with repetition allowed and no indistinguishable objects.
The lecturer can enter the room in 3 ways and exit in 3 ways. So, in total, the lecturer can enter and leave the room in 9 (= 3 * 3) ways. The answer is (D). This problem allows repetition: the lecturer can enter by a door and exit by the same door.
Hope this helps.
Regards
The lecturer can enter and exit through the same door, repetition is allowed.
Doors are different. They are not indistinguishable, so no indistinguishable objects. Hence, we have a permutation problem, with repetition allowed and no indistinguishable objects.
The lecturer can enter the room in 3 ways and exit in 3 ways. So, in total, the lecturer can enter and leave the room in 9 (= 3 * 3) ways. The answer is (D). This problem allows repetition: the lecturer can enter by a door and exit by the same door.
Hope this helps.
Regards
