# Can Cinderella avoid dancing with her stepfamily?

Level pending

Ref: Disney Japan

Cinderella is at a ball with 49 other people. While dancing, they form 25 pairs (with 2 people in each pair). However, Cinderella really wants to avoid her evil stepmother and 2 ugly stepsisters (total of 3 people), and does not want to dance with any of them.

If there are $$N$$ ways to form 25 pairs for dancing in which Cinderella doesn't have to dance with any of her stepfamily, what are the last 3 digits of $$N$$?

Details and assumptions

There are no gender restrictions for the dancing pairs.

The order of the pairs does not matter.

Calculators are allowed for this question. I'm not that mean ^_^.

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