2.1.5.
(a)
There
are
C!.r:4
waln of
picking
depdrtments.
For
depart_
ment
choices
berow,
.'"
iil
trr"
t"i'.r
;;;;".
of
commitees
from
those
de.
partments,
by
using
the counting
;;tr.;l;,
{1,2,3}
:.4
._4
.5
:
8oi
{t,2,4}
:
4.
4
.5
:
8oi
{1,3,4}
:
4.
s.5
:
roo;
ii,i,nl
:
4.
5.5
:
1oo.
ilTj"j$:tmber
of
possible
committees
is
then
the
sum
80
+
80
+
100
+
(b)
The
committe
conditions.
r,o.
"*u.il]enot.equally
lil,ely
under
the
specified
selection
parrment
2,
an
d,
i.':ii'
j:,
r:::ff
"l "r*:F"1",T:ffi**"
t,:
5
i$:Iil:ilrc3mbination'
,r'""
."r".;
;*
three
indiviiuui,"io*
,r,oru
P[z
from
departmt
'"'
t:'*1?T.Tiif:*J
2,
z
rromdepartment
3l
But
for the other
department"""ri,o,l*l"r*
*
P[r
from
department
l,
y
from
departme
:
l

rl
.
t.:r
"tf
2'z
from
department
4J
4 \4
L s)_Tfr.
P[z from
department
1,
9,fr9T
department
3,
z from department
4l
C/i*
I
pfc
from
denarrman+
,
".1]i
:t
+'
=
#,
ar
ot4,
efl#w3
Tllbf/?+kt
.
/lt'
t,/
o?+/z
ry{+}4/f
Ui1Ua"rl
d4a/^
ter
t
P[c
department
2,
y
from
departn
rndividua,sd**h;;;i,i,:,:t'tt':::il.:":"T::,:,,
multiply
the probabititv
i/+ rr,.i1i"'ai"l
abilitv
i
n
at
t
r,e
in
a..,i
q
u
"r'
t
"
il"
o'"o''";11:"',",
:'u
jj
$iji
lo:
rl"r*
3;f;I*"
I
and
2'
Uut
oo'rviziiJ.l.o"',*ents
3
and
4.
(3/16
vs.
,
x
I
2.L.25.
Assume
that
the
fifteea subjects are
indistinguishable
The
prob
since
this
is
a
bit
less
than
8%, we have
a
little
evidence
that
brand
selec'
lem is
to
couut
tbe
number
of
ways
that
15 such
subjects,
positioned
in
a
row,
ca'
be
split
into
3
goups.
As
in
Fig'
2'2, do
tbe
partitioning
l/,0 f
,
"
by
inserting
two
special markers
into
the
list
aaywhere.
Then
there
are
'.'",,:6.
fS
+
Z
=
1?
positions
in
the
new
list,
and
a
partition correspol&
"iiqY*
ifnff8:'"]:
to
a
selection
of
2
positions
for
the markeis'
wbich can
e o"TrTrfil
t/d*&
ways.