Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter, she prepared an envelope with its complete address. If the 4 letters are to be put into the 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address ?
A. 1/24
B. 1/8
C. 1/4
D. 1/3
E. 3/8
With all these letters and envelopes things together I lost my way !!
Probability of 1 of 4 letters reaching right addressed env
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- utkalnayak
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- utkalnayak
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- GMATGuruNY
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Let the 4 letters be A, B, C and D.utkalnayak wrote:Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter, she prepared an envelope with its complete address. If the 4 letters are to be put into the 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address ?
A. 1/24
B. 1/8
C. 1/4
D. 1/3
E. 3/8
Total ways to arrange the 4 letters = 4! = 24.
Let the correct ordering of the 4 letters be ABCD.
Write out the ways that ONLY A can be put in the correct position:
ACDB
ADBC
Total ways = 2.
Using the same reasoning, there will be 2 ways that ONLY B can be put in the correct position, 2 ways that ONLY C can be put in the correct position, and 2 ways that ONLY D can be put in the correct position.
Thus, the total number of ways to put EXACTLY 1 letter in the correct position = 2+2+2+2 = 8.
Thus:
P(exactly 1 letter is put in the correct position) = 8/24 = 1/3.
The correct answer is D.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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- utkalnayak
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In the above case why you think there are only 2 possibilities in each case ?GMATGuruNY wrote: Write out the ways that ONLY A can be put in the correct position:
ACDB
ADBC
Total ways = 2.
Using the same reasoning, there will be 2 ways that ONLY B can be put in the correct position, 2 ways that ONLY C can be put in the correct position, and 2 ways that ONLY D can be put in the correct position.
Thus, the total number of ways to put EXACTLY 1 letter in the correct position = 2+2+2+2 = 8.
Thus:
P(exactly 1 letter is put in the correct position) = 8/24 = 1/3.
The correct answer is D.
Should it not be 3! ways ?
Thanks,
Utkal
Utkal
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Hi utkalnayak,
In this prompt, you have 2 conditions that have to be met:
1) JUST 1 letter is put in the correct envelope
2) The other 3 letters must be put in an INCORRECT envelope.
IF...."A" is properly placed in the "A" envelope, B CANNOT be put in the "B" envelope, C CANNOT be put in the "C" envelope and D cannot be put in the "D" envelope. Those other rules still have to be accounted for.
Mitch's solution correctly accounts for BOTH conditions.
GMAT assassins aren't born, they're made,
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In this prompt, you have 2 conditions that have to be met:
1) JUST 1 letter is put in the correct envelope
2) The other 3 letters must be put in an INCORRECT envelope.
IF...."A" is properly placed in the "A" envelope, B CANNOT be put in the "B" envelope, C CANNOT be put in the "C" envelope and D cannot be put in the "D" envelope. Those other rules still have to be accounted for.
Mitch's solution correctly accounts for BOTH conditions.
GMAT assassins aren't born, they're made,
Rich
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