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04 Dec 2014, 03:16
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
90% (00:48) correct
10%
(01:34)
wrong
based on 134
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5 letters have to be put into their 5 respective envelopes. If the letters are inserted randomly into the envelopes, what is the probability that all the letters go into their respective envelopes?
A) 1/30
B) 1/60
C) 1/120
D) 1/240
E) 3/5
A) 1/30
B) 1/60
C) 1/120
D) 1/240
E) 3/5
04 Dec 2014, 03:37
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desaichinmay22
let 5 envelopes be E1,E2,E3,E4,E5. now first letter can go to any of 5 envelopes in 5 ways. second letter can go to any of the 4 remaining envelopes in 4 ways. third letter can go to remaining 3 envelopes in 3 ways. fourth letter can go to remaining 2 envelopes in 2 ways. and finally last envelopes has only 1 ways.
so when no restrictions are applied. these 5 letters can arrange themselves in 5 envelopes in 5.4.3.2.1=120 ways
(we can also think of this as arrangements of 5 students in 5 vacant spaces.)
now, obviously there is only one correct envelope designated for each letter. thus the number of ways in which all letters will be correctly posted=1
thus required probability = 1/120
04 Dec 2014, 04:04
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desaichinmay22
A-B-C-D-E (envelopes)
a-b-c-d-e (letters)
5 letters (a, b, c, d, and e) can be assigned to 5 envelopes (arranged) in 5! ways, out of which only one will be correct, thus the probability is 1/5! = 1/120.
Answer: C.
