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07 May 2025, 03:40
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
60% (01:30) correct
40%
(01:38)
wrong
based on 209
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Hitesh has a row of 6 hangers on which he can hang his formal shirts. He has 3 identical white shirts, and one blue shirt to hang on the hangers. In how many different orders could he hang the shirts on the hangers?
A. 4
B.30
C. 60
D. 120
E. 360
A. 4
B.30
C. 60
D. 120
E. 360
07 May 2025, 10:25
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Hi Guys, Correct me if my reasoning is somehow wrong, I considered how I could get 4 hangers out of 6: 6!/4!2!, then I considered how these 4 could be placed considering that there are 3 identical items:4!3! to come up with 15*4 so 60
Aabhash777
14 May 2025, 22:44
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I did it in a little weird way, so I'm not sure if others would solve like this but here goes:
First, find out how to arrange 3 white shirts and 1 blue shirt when order DOES matter: 4!/3! = 4.
Now we need to figure out how to pick 4 hangers to hang the shirts from out of the 6: 6C4 = 15. (Alternatively, figure out how to pick 2 hangers to NOT hang shirts from = 6C2 = 15).
For each way to pick 4 hangers there's 4 ways to arrange the colored shirts, so 4*15 = 60
First, find out how to arrange 3 white shirts and 1 blue shirt when order DOES matter: 4!/3! = 4.
Now we need to figure out how to pick 4 hangers to hang the shirts from out of the 6: 6C4 = 15. (Alternatively, figure out how to pick 2 hangers to NOT hang shirts from = 6C2 = 15).
For each way to pick 4 hangers there's 4 ways to arrange the colored shirts, so 4*15 = 60
