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Committee Choice Concern (Posted on 2010-05-17) Difficulty: 3 of 5
A committee of 5 is to be chosen from a group of 9 people.

Determine the total number of ways this can be accomplished, given that:

(i) Harold and Warren must serve together or not at all, and:

(ii) Lucy and Deanna refuse to serve with each other.

No Solution Yet Submitted by K Sengupta    
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Solution Solution Comment 3 of 3 |

There are six possibilities for the specific four people mentioned: either none on a given committee  or one of the following sets: HW, L, D, HWL, HWD. The remaining committee members must come from the other 5 members. The numbers are as follows:

None: C(5,5) =  1
HW:   C(5,3) = 10
L:    C(5,4) =  5
D:    C(5,4) =  5
HWL:  C(5,2) = 10
HWD:  C(5,2) = 10
              ---
               41


              
So there are 41 possible committees. 

Computer verification:

Members are designated by 1 thru 5 and HWDL.

12345
1234L
1234D
1235L
1235D
123HW
1245L
1245D
124HW
125HW
12HWL
12HWD
1345L
1345D
134HW
135HW
13HWL
13HWD
145HW
14HWL
14HWD
15HWL
15HWD
2345L
2345D
234HW
235HW
23HWL
23HWD
245HW
24HWL
24HWD
25HWL
25HWD
345HW
34HWL
34HWD
35HWL
35HWD
45HWL
45HWD
 41
 
produced by

DECLARE SUB choose (psn!)
DIM SHARED memb$, cmtee$, ct

memb$ = "12345HWLD"
choose 1
PRINT ct

SUB choose (psn)
   IF psn = 1 THEN st = 1
   IF psn > 1 THEN
    ix = INSTR(memb$, RIGHT$(cmtee$, 1))
    st = ix + 1
   END IF
   FOR choice = st TO 9
     good = 1
     ch$ = MID$(memb$, choice, 1)
     IF ch$ = "L" AND INSTR(cmtee$, "D") > 0 THEN good = 0
     IF ch$ = "D" AND INSTR(cmtee$, "L") > 0 THEN good = 0
     IF good THEN
       cmtee$ = cmtee$ + ch$
       IF psn = 5 THEN
         IF INSTR(cmtee$, "H") > 0 AND INSTR(cmtee$, "W") = 0 THEN good = 0
         IF INSTR(cmtee$, "W") > 0 AND INSTR(cmtee$, "H") = 0 THEN good = 0
         IF good THEN PRINT cmtee$: ct = ct + 1
       ELSE
         choose psn + 1
       END IF
       cmtee$ = LEFT$(cmtee$, psn - 1)
     END IF
   NEXT
END SUB

 


  Posted by Charlie on 2010-05-17 14:51:59
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