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About LinkBacksA secretary types 4 letters and then addresses the 4 corresponding envelopes. In how many ways can the secretary place the letters in the envelopes so that NO letter is placed in its correct envelope
A.8
B.9
C.10
D.12
E.15
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A secretary types 4 letters and then addresses the 4 corresponding envelopes. In how many ways can the secretary place the letters in the envelopes so that NO letter is placed in its correct envelope
A.8
B.9
C.10
D.12
E.15
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None match the answer
Should be 23
Total ways of putting 4 letters in 4 envelopes (assuming an envelope can only hold one letter) = 4 * 3 * 2 *1 = 24
Total ways of putting all letters in their correct envelopes = 1
Total ways of NOT putting them correctly = 24 -1 = 23
Last edited by rookie2005; 12-17-2005 at 09:01 PM.
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E?
4*4=16 ways.
Correct way = 1.
16-1=15
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I agree with this soln.Originally Posted by rookie2005
good one rookie.
I am told that i talk in shorthand & then smudge it.
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Agree with Ankost.
Should be 15.
Total ways of putting 4 letters in 4 envelopes cant be 4!.
The first letter can be put in any one of the envelope in 4P1 ways.
Similary the 2nd letter can be put in any one of the envelope in 4P1 ways (and not 3P1)
3rd letter in 4P1 ways and the 4rth letter in 4P1 ways.
Total number of ways = 4+4+4+4 = 16.
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But once you put the first letter isn't there a reduced sample space???
I am told that i talk in shorthand & then smudge it.
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The total number of ways of putting 4 letters into 4 envelopes can be
1) Case where an envelope can take any number of letters, ie some may be empty and others might have more than 1 = 4*4*4*4 = 4^4
2) Case where every envelope must have atleast one letter
= 4*3*2*1 = 24
Why is everyone adding 4 + 4 +4 +4 , Please explain
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Ways to have no letter in its correct envelope = Total ways of enveloping - Number of ways to envelope atleast 1 letter correctly.
Total ways = 4! = 24
Correct - Incorrect:
1 - 3
Number of ways to envelope 3 letters incorrectly (all incorrect) = 2
=> total number of 1-3 combos = 4*2 = 8
2 - 2
Number of ways to envelope 2 letters incorrectly (all incorrect) = 1
=> total number of 2-2 combos = 4C2*1 = 6
4 - 0
Number of 4-0 combos = 1
Note: It's important to realize that a 3-1 (correct-incorrect) combo is impossible.
So, Ways to have no letter in its correct envelope = 24 - (8+6+1) = 9
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very cool Arjmen!
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