258 ON THE GAME OF MOUSETRAP. [672 
Classifying these so as to show in how many arrangements a given card or permutation 
of cards is thrown out, we have the table 
No. Thrown out. 
9 none 
4 1 
1 3 
2 4 
1 
3, 
2 
1 
2, 
3 
1 
3, 
4 
1 
1, 
3, 
4, 
2 
1 
1, 
2 
3, 
4 
1 
I) 
2, 
C 
3 
1 
2, 
1, 
3, 
4 
1 
3, 
1, 
2, 
4, 
24, 
r iz. there are nine arrangements in which 
no 
card 
is 
thrown out, four arrangements 
in which only the card 1 is thrown out, one arrangement in which only the card 3 
is thrown out, and so on. 
It will be observed that there are five arrangements in which all the cards are 
thrown out, each throwing them out in a different order ; there are thus only five 
orders in which all the cards are thrown out. 
The general question is of course to form a like table for the numbers 5, 6, ..., 
or any greater number of cards.