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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 just counting | Comment 1 of 3
 

Answer: 30

 

 

SOLUTION:

CASE 1:   HWL, notD  We have 3 in and select another 2  out of 5  i.e. 10

CASE 1' HWD, notL   ....   same thing

Case 2 L, notD &not HW   4 needed out of 5     i.e. 5

Case 2' D, notL &not HW  ..... same thing

 

2*10+2*5=30

oops!  Without both ladies:

Two more cases, in addition to Ady's:


Case 3: HW, not D or L: select another 3 out of 5, ie 10
Case 3': Not HW, not D or L: select 5 out of 5, equal 1

So, previous 30, + 10 + 1 = 41
 
The correct answer:  41

Edited on May 17, 2010, 5:14 pm
  Posted by Ady TZIDON on 2010-05-17 14:13:17

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