1 votes 1 votes in how many ways 6 letters can be placed in 6 envelopes such that at least 4 letters go into their corresponding envelopes ? Combinatory discrete-mathematics combinatory made-easy-test-series + – ronin_codex asked Jan 19, 2019 • edited Mar 3, 2019 by ajaysoni1924 ronin_codex 1.0k views answer comment Share Follow See all 14 Comments See all 14 14 Comments reply Manas Mishra commented Jan 19, 2019 reply Follow Share 22? 0 votes 0 votes Shubhanshu commented Jan 19, 2019 reply Follow Share 16? 1 votes 1 votes Kunal Kadian commented Jan 19, 2019 reply Follow Share 30 ? 0 votes 0 votes muthu kumar commented Jan 19, 2019 reply Follow Share Yeah! it should be 30 0 votes 0 votes Shubhanshu commented Jan 19, 2019 reply Follow Share Explanation? 0 votes 0 votes Kunal Kadian commented Jan 19, 2019 reply Follow Share First we will select 4 letters from 6 and assign them to their respective envelopes. i.e. $^4C_2$ Then for remaining 2 letters there are 2! ways Therefore 30 0 votes 0 votes muthu kumar commented Jan 19, 2019 reply Follow Share Atleast 4 in right place. So, selecting 4 out of 6 in 6C4 ways. remaining two can come in two ways either arranged or not. 6C4 * 2 = 15*2 = 30 0 votes 0 votes Shubhanshu commented Jan 19, 2019 reply Follow Share You forgot to apply inclusion exclusion principle. Suppose u put letter 1,2,3,4 into their respective envelopes now u r remaining with letter 5 and 6 which can be placed in Envelop 6 and 5 only. Means only one choice l. So it will be C(6,4). And the last one when all are in there respective envelopes. Hence total should be 15+1=16. 3 votes 3 votes muthu kumar commented Jan 19, 2019 reply Follow Share Bro, atleast 4 right? it is not atmost 4 0 votes 0 votes Kunal Kadian commented Jan 19, 2019 reply Follow Share @Shubhanshu Yes, CORRECT! The answer should be $16$. Thanks. 0 votes 0 votes Shubhanshu commented Jan 19, 2019 reply Follow Share Yes muthu Kumar 0 votes 0 votes muthu kumar commented Jan 19, 2019 reply Follow Share @Shubhanshu Thanks bro. understood 0 votes 0 votes Kunal Kadian commented Jan 19, 2019 reply Follow Share @muthu kumar Answer is not 30 bcoz, when you do $^4C_2$ and select say 1,2,3,4, then according to you there are 2 combinations,.. 1,2,3,4,5,6 and 1,2,3,4,6,5 Now if you select say 3,4,5,6 then also according to you there are 2 combinations.. 1,2,3,4,5,6 and 2,1,3,4,5,6 Look here 1,2,3,4,5,6 is repeating.. 0 votes 0 votes muthu kumar commented Jan 19, 2019 reply Follow Share Yeah bro. Understood. 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes Exactly 4 in correct place = 6C4 * D2 = 15 Exactly 5 in correct place = 6C5 * D1 = 6 Exactly 6 in ocrrect place = 1 Total no of ways = 22 suvradip das answered Jan 16, 2020 suvradip das comment Share Follow See all 2 Comments See all 2 2 Comments reply Jungan95 commented Jan 30, 2020 reply Follow Share Answer should be 16. When you consider the case of exactly 5 in correct places, the 6th one is automatically in its correct place. Therefore, 15+1=16. 2 votes 2 votes priyesh9875 commented Jan 30, 2020 reply Follow Share If we have 5 letters in correct places, then 6th one has only 1 place to go, which is its correct place. So answer should be 16 0 votes 0 votes Please log in or register to add a comment.