Question

Fifteen married couples are at a dance lesson, but now only five men and five women are selected at random, then randomly paired. (a) What is the number of possible dancing arrangements?

Answer 1

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!

= $[\frac{15!}{5!\times(15-5)!}]^2$ × ( 5 × 4 × 3 × 2 × 1 )

= $[\frac{15\times14\times13\times12\times11\times10!}{5\times4\times3\times2\times1\times10!}]^2$ × ( 5 × 4 × 3 × 2 × 1 )

= $[\frac{360360}{120}]^2$ × 120

= 1082161080