top button
Flag Notify
    Connect to us
      Facebook Login
      Site Registration Why to Join

    Get Free Puzzle Updates

Facebook Login
Site Registration

In how many ways can all of the letters be placed in the wrong envelopes?

+3 votes
392 views

A correspondent writes 7 letters and addresses 7 envelopes, one for each letter. In how many ways can all of the letters be placed in the wrong envelopes?

posted Sep 22, 2015 by anonymous

Share this puzzle
Facebook Share Button Twitter Share Button Google+ Share Button LinkedIn Share Button Multiple Social Share Button

4 Answers

+2 votes

Answer: 1854

1 letter, 0 way
2 letters, 1 way
3 letters, 2 ways
4 letters: 9 Ways 3*2=6 ways of cycling the 4 around, but then 3 ways of doing 2+2. (=9)

So partitioning is the way to go. A partition of 1 always maps the letter into the right envelope, so there's no answers with partition 1.

7 can be
a "cycle" of 7: with 1 case, which has 6*5*4*3*2 permutations
a "cycle" of 5 plus a "cycle" of 2: with 7*6/2 cases and 4*3*2 permutations
a "cycle" of 4 plus a "cycle" of 3: 7*6*5/6 cases and (2 {for the 3} * 9 {for the 4}) permutations
i.e. 720+504+630=1854

Or we can use formula
7! * ( 1/2! - 1/3! + 1/4! - 1/5! + 1/6! - 1/7! )
= 2520 - 840 + 210 - 42 + 7 - 1
= 1854

answer Sep 23, 2015 by Maninder Bath
+1 vote
E1 E2 E3 E4 E5 E6 E7 
L1 L2 L3 L4 L5 L6 L7

Now assume L1 can be put into 7 ways into an envelope and only one is correct and 6 are wrong ways similarly for L2 there are six ways and so on
So total possible wrong ways are 6*6*6*6*6*6*6
=) 6^7 or 279936

answer Sep 22, 2015 by Salil Agrawal
No. As u said, there are 6 ways in which L1 will not be placed in E1. But for example, say L3 is placed in E1, then in E2 we cannot place both L3 and L2 (Since L3 is already placed in E1), so now the chances reduces to 5 and not.
Yes you are right the number of possible ways would be 6! i.e. 6.5.4.3.2.1 :)
+1 vote

7!
IN 5040 WAYS.

answer Oct 2, 2015 by Naga Jyothi
+1 vote

Ms Naga Jyothi, please remember that of the 5040 ways only one is true. Hence the answer is 5039

answer Dec 30, 2016 by Kewal Panesar



Similar Puzzles
+1 vote

How many ways can n books be placed on k distinguishable shelves?
a. If no two books are the same ,and the positions of the books on the shelves does not matter?
b. If no two books are the same,and the positions of the books on the shelves matter?

+2 votes

There are 12 different chocolates placed on a table along a straight line. In how many ways can a person choose 4 of them such that no 2 of the chosen chocolates lie next to each other?

0 votes

In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?

0 votes

In how many ways the letters of the word ‘CHEKOSLOVAKIA’ can be arranged such that “SL” always comes together and ‘H’ and ‘I’ at the end places?

Contact Us
+91 9880187415
sales@queryhome.net
support@queryhome.net
#280, 3rd floor, 5th Main
6th Sector, HSR Layout
Bangalore-560102
Karnataka INDIA.
QUERY HOME
...