Infinite Series , 
1 7 1 
4 ■# 
« s 
^ * <3 — # . — 2 X . .a — n — %xx(b % b x -\rcxc — x 
. d-x^-Scc. + 260+26'^+ zed + See.') t . . . . +Lx(^. 
a — x.a-zx*..a - / - i xxb.b~x.b-2x . . b-m—ix 
X c . c — x • £ — 2 ^ x, , c p ~ i xycd'd~ B X*d~- 2x . . e 
d - q - IX X See. - K) +&C., where L«=# . 
»*— I w — 2 
# — /+ I 
n — l * 
k — /— - 1 
— 2 n — l— m 4* i 
/ . 2 
jf — / — > 7 ? — I n — l—m— 2 
3 272 
« — / — m*—p -l - 1 
~ 7 ' 
X n - l ~~ m • 
X n ~ l - m - p . 
a 3 
I n-l-m—p — 2 ^ ^ y &C. which is 
2 3 ? 
the fame as the co-efficient of the term d' x b" x c? x d* 
X &c. in the multinomial <? + £ + c + i+ &c. raifed to the 
power ». 
The chance of any number of events A, B, C, D, &c. of 
which the numbers are a, b , c, </, &c. happening /, z», q , &c. 
times refpeclively in a fimilar manner to A’s and B’s happening in 
the preceding cafe will be - . 
All the propofitions mentioned as immediately deducible 
from the preceding theorem may, mutatis mutandis, with the 
fame eafe be applied to more events A, B, C, D, &c. 
If for a, b, c, d, &c. be fubftituted the fame letters, in- 
creafed or diminiffied by any given quantities, the refulting 
equation will be equally true. 
A a 2 
E H- 
