Word to Number

What number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain




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I have thought of a number that is made up by using all the ten digits just once. Here are a few clues for you to guess my number:

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Amazing Facts

Gamers

In 2011, people playing Foldit, an online puzzle game about protein folding, resolved the structure of an enzyme that causes an Aids-like disease in monkeys. Researchers had been working on the problem for 13 years. The gamers solved it in three weeks.