A dance delegation of 4 people must be chosen from 5 pairs of dance partners. If 2 dance partners can never be together on the delegation, how many different ways are there to form the delegation?  Choose one:
A) 20
B) 30
C) 60
D) 70
E) 80
Since 2 dance partners can never be together, lets select 4 pairs from 5 pairs of dance partners to fill the 4 positions. Now, in each position, each pair can be selected in 2 different ways.   Therefore number of ways of forming a delegation such that the 2 dance partners are never together = 5C4*(2C1)^4 = 5 * 16= 
<gadget id="calculator">5 * 16</gadget>
<output>80</output>
80   Answer: 80
<result>E</result>
A dance delegation of 4 people must be chosen from 5 pairs of dance partners. If 2 dance partners can never be together on the delegation, how many different ways are there to form the delegation?