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.

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 ¬ HW 4 needed out of 5 i.e. 5

Case 2' D, notL ¬ 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**