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Isha2701
“Without replacement” means that once a number is chosen, it is removed from the pool, so it cannot be chosen again and the next denominator drops from 20 to 19, then 18, and so on. Your mistake is using 5!: the three “any” positions are not distinct, so swapping those among themselves does not create new cases, which is why you count only 5!/3! = 20 arrangements, not 120.
For more please review the rest of the discussion.
