How do you do this?

<p>When the three Adams children went to school one morning, they each took one of the others' lunches. In how many ways could the three children have been paired with the lunches so that no one took his or her own?</p>

<p>1
2
3
6
8</p>

<p>Why is it 2</p>

<p>lunch ABC</p>

<p>person ABC</p>

<p>person A can only take lunch B,C
if he takes Lunch B.
Person B, must take lunch C, because person C cannot take lunch C.</p>

<p>If person A takes Lunch C, then person B must take Lunch A.</p>

<p>so 2 ways. I know my explanation sucks, but its right</p>

<p>WE have three children
A B C , they don't take their own lunches
a b c represent the respective lunches to each kid
So if you have
Ab then Bc and Ca thats the ONLY way
But if you have
Ac Ba Cb. This is also the only way
Hence 2 ways.</p>

<p>Why can't A take c and B take a and C take b</p>

<p>there's a much easier way to do this...there are only 2 opportunities for each person...therefore, 2! = 2</p>

<p>but how do you know when to use ! symbol</p>

<p>r3n did you even read my explanation.</p>

<p>did you read mine though? The one below yours</p>

<p>I SAID A take C B take a And C take b. Are you being sarcastic?</p>

<p>if A takes B, then B must take C and C has A</p>

<p>if A takes C, B must take A, and C takes B</p>