Answer:
( ¹⁵C₂ )² × 5! = 1082161080
Explanation:
Data provided in the question:
Number of married couples = 15
Therefore,
Number of males = 15
Number of females = 15
Now,
The number of possible dancing arrangements
= Probability of selecting males × Probability of selecting males × ways of arranging 5 pairs
= ¹⁵C₂ × ¹⁵C₂ × 5!
= ( ¹⁵C₂ )² × 5!
= [tex][\frac{15!}{5!\times(15-5)!}]^2[/tex] × ( 5 × 4 × 3 × 2 × 1 )
= [tex][\frac{15\times14\times13\times12\times11\times10!}{5\times4\times3\times2\times1\times10!}]^2[/tex] × ( 5 × 4 × 3 × 2 × 1 )
= [tex][\frac{360360}{120}]^2[/tex] × 120
= 1082161080
