Problem 27 (counting committees)
This is given by the multinomial coe
ffi
cient
12
3
,
4
,
5
= 27720
Problem 28 (divisions of teachers)
If we decide to send
n
1
teachers to school one and
n
2
teachers to school two, etc. then the
total number of unique assignments of (
n
1
, n
2
, n
3
, n
4
) number of teachers to the four schools
is given by
8
n
1
, n
2
, n
3
, n
4
.
Since we want the total number of divisions, we must sum this result for all possible combi
nations of
n
i
, or
n
1
+
n
2
+
n
3
+
n
4
=8
8
n
1
, n
2
, n
3
, n
4
= (1 + 1 + 1 + 1)
8
= 65536
,
possible divisions.
If each school must receive two in each school, then we are looking for
8
2
,
2
,
2
,
2
=
8!
(2!)
4
= 2520
,
orderings.
Problem 29 (dividing weight lifters)
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 Winter '08
 G.JOGESHBABU
 Counting, Probability, weight lifters

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