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Q: 4 letters are to be put into 4 envelopes . what is the probability that out of 4 only one letter goes into the envelope with its correct address.
a)1/24
b)1/8
c)1/3
d)1/4
e)3/8
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Hi romitrock,
Sometimes complex-looking questions can be 'played with'; in that way, you might be able to find the pattern that the question is built around (and you won't have to do all of the work).
With 4 letters, there are 4! = 24 different arrangements (for the letters to be put into the envelopes). Let's 'map out' the options assuming that the "A" letter is placed in the first envelope (the "A" envelope), with the 2nd ("B" envelope), 3rd ("C" envelope) and 4th ("D" envelope) following. Those options would be....
ABCD
ABDC
ACBD
ACDB
ADBC
ADCB
So there are 6 options here; how many of them have JUST ONE letter in the proper envelope?
ABCD = all 4 of them
ABDC = 2 of them
ACBD = 2 of them
ACDB = JUST 1
ADBC = JUST 1
ADCB = 2 of them
So 2 out of these 6 options 'fit' what we're looking for. 2/6 = 1/3. Now the question is whether that pattern is consistent or not.... What happens when you place the B in the "A" envelope....?
BACD
BADC
BCAD
BCDA
BDAC
BDCA
How many of these options 'fit' what we're looking for?....
You'll find that the pattern is consistent, so there's no need to check the other options (C in "A" envelope and then D in the "A" envelope). We have enough evidence to deduce that 1/3 of all of the options will 'fit' what we're looking for.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
Sometimes complex-looking questions can be 'played with'; in that way, you might be able to find the pattern that the question is built around (and you won't have to do all of the work).
With 4 letters, there are 4! = 24 different arrangements (for the letters to be put into the envelopes). Let's 'map out' the options assuming that the "A" letter is placed in the first envelope (the "A" envelope), with the 2nd ("B" envelope), 3rd ("C" envelope) and 4th ("D" envelope) following. Those options would be....
ABCD
ABDC
ACBD
ACDB
ADBC
ADCB
So there are 6 options here; how many of them have JUST ONE letter in the proper envelope?
ABCD = all 4 of them
ABDC = 2 of them
ACBD = 2 of them
ACDB = JUST 1
ADBC = JUST 1
ADCB = 2 of them
So 2 out of these 6 options 'fit' what we're looking for. 2/6 = 1/3. Now the question is whether that pattern is consistent or not.... What happens when you place the B in the "A" envelope....?
BACD
BADC
BCAD
BCDA
BDAC
BDCA
How many of these options 'fit' what we're looking for?....
You'll find that the pattern is consistent, so there's no need to check the other options (C in "A" envelope and then D in the "A" envelope). We have enough evidence to deduce that 1/3 of all of the options will 'fit' what we're looking for.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
