92 BIOMETRY 
And it is clear that any one of these combinations is 
equally likely to appear on any given occasion, if the 
coins are supposed to be strictly symmetrical, and are 
tossed up entirely at random. Now, the second and 
third results are the same unless the two coins are indi- 
vidually distinguishable. So we may write the most 
likely result of tossing up two pennies four times in the 
following way : 
1HH+2HT+1TT. 
And in a similar way we may discover that the most 
likely result of tossing up three coins eight times is : 
IHHH+3HHT+3HTT+1TTT. 
In the first case H T is twice as likely to appear as 
H Hat any single throw, and in the second case H H T 
is three times as likely as H H H in any single toss. 
It is possible to work out the most probable relative 
frequency of the various possible combinations in the 
case of any number of coins. Thus for ten coins the 
sequence of numbers runs : 
TABLE II. 
Heads. Tails. Prbatilty. 
10 ° I 
9 I Io 
8 2 45 
7 3 120 
6 4 210 
5 5 252 
4 6 210 
3 7 120 
2 8 45 
I 9 10 
l fe} 10 I 
