1 votes 1 votes closed as a duplicate of: GATE CSE 2010 | Question: 65 Given digits 2,2,3,3,3,4,4,4,4 how many way distinct 4 digit numbers greater than 3000 can be formed? a)50 b)51 c)52 d)54 Ipsita Priyadarsini asked Sep 5, 2017 closed Sep 5, 2017 by LeenSharma Ipsita Priyadarsini 416 views comment Share Follow See all 3 Comments See all 3 3 Comments reply saxena0612 commented Sep 5, 2017 reply Follow Share https://gateoverflow.in/2373/gate2010-65 0 votes 0 votes Akash Verma 1 commented Sep 17, 2017 reply Follow Share Given digits= 2,2,3,3,3,4,4,4,4 As the number is greater than 3000. So thousand place can be filled by only 3 or 4 so case 1: when thousand place start with 3 3 a b c a,b,c can be filled with 2 or 3 or 4 each in 3 ways . so 3 * 3 * 3 = 27 number are there but 3333 and 3222 are not possible then total ways = 27 - 2 (invalid number cause Here number of 2's is not 3 & number of 3's is not 4 ) = 25 ways case 2: when thousand's place start with 4 4 a b c a,b,c can be filled with 2 or 3 or 4 each in 3 ways . so 3 * 3 * 3 = 27 number are there but 4222 is not possible then total ways = 27 - 1 (invalid number cause Here number of 2's is not 3) = 26 ways Then, total ways( distinct 4 digit numbers greater than 3000) = 25 + 26 = 51 ans 1 votes 1 votes Ipsita Priyadarsini commented Sep 18, 2017 reply Follow Share Thank you 0 votes 0 votes Please log in or register to add a comment.