abhishek wrote 6 letters to 6 friends. He wants to post these in addressed envelops. By how many ways 4 letters have gone into wrong envelops?
Can you check the problem at http://courses.manishverma.site/mod/forum/discuss.php?d=2071#p5832 !
Hi,
Let us first post the 2 letters which have to go to the correct envelopes. The number of ways of selecting which are the lucky two will be 6C2. The number of ways of putting them into their envelopes will be 1 for both.
Now, we are left with four letters and four envelopes, none of which have to go into the corresponding envelope. For those of you who do not know, there is a term called a "sub-factorial" which is the number of permutations n things such that none of them appear in their natural place. It is denoted by (!n) rather than (n!) which is for factorial. Google it ( I prefer mathworld.wolfram.com)
So, for you the answer would be: 6C2 * !4 = 15 * 9 = 135.