A warehouse printer makes an 8-digit shipment label by joining six pre-printed strips end-to-end. Four strips have one digit on them: 0, 1, 2, 9. Two strips have two digits on them: 19 and 20. Each strip must be used exactly once, and the final label is invalid if its first digit is 0.
How many valid labels can the printer produce?
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grouping the specific, the group sizes can be only 5, 2 and 1. so we have multiple cases such as
6 distinct labels come from exactly 4 permutations each
96 distinct labels come from exactly 2 permutations each
504 distinct labels come from exactly 1 permutation each
(504x1)+(96x2)+(6⋅4)=720
and total distinct 8-digit labels = number of classes = 504+96+6=606
now we remove the ones starting with 0 that removes 5! possibilities
606-120=498
I kinda skimmed through with writing the reasoning because I was bored