1 votes 1 votes How many license plates consisting of three letters followed by three digits contain no letter or digit twice? Combinatory counting discrete-mathematics + – Swati001 asked Aug 20, 2016 • edited Jun 25, 2019 by srestha Swati001 2.8k views answer comment Share Follow See 1 comment See all 1 1 comment reply dd commented Aug 20, 2016 reply Follow Share Considering possibel letter set as english alphabet (small or capital but not both = 26 letters) and digits (0,1,...9) We can have 26*25*24*10*9*8 = 11232000 0 votes 0 votes Please log in or register to add a comment.
3 votes 3 votes So, every letter and digit must be unique. $26 \times 25 \times 24 \times 10 \times 9 \times 8$ Arjun answered Aug 20, 2016 Arjun comment Share Follow See all 4 Comments See all 4 4 Comments reply Swati001 commented Aug 20, 2016 reply Follow Share Yes Sir answer is correct but i thought that is the possible answer when qstn is NO letter and NO digit twice it says OR so suppose ABC112 doesnt count here ? No letter twice or no digit twice Inclusion Exclusion principle. Is it not applicable here ? 0 votes 0 votes Arjun commented Aug 20, 2016 reply Follow Share Nopes. That is the ambiguity of English language. We have to apply the common meaning as per English. contain no letter or digit twice means no 2 letters allowed AND no 2 digits allowed. We should parse the sentence as contain no ((letter or digit) twice) contain no (letter twice or digit twice) contain no letter twice and contain no digit twice When negation comes inside, AND/OR are reversed - DeMorgan's principle. This is applied in many questions. 2 votes 2 votes Swati001 commented Aug 20, 2016 reply Follow Share yes got it.sir . Doubt cleared :) 1 votes 1 votes monanshi commented Mar 3, 2018 reply Follow Share Sir, what if the mean only twice (but, we can have thrice)? What will be the answer in that case? 0 votes 0 votes Please log in or register to add a comment.