0 votes 0 votes If A = {1,2,3 …. n} then how many multisets of size 4 are possible ,such that atleast of the elements appears twice. Mathematical Logic graph-theory + – manisha11 asked Jan 2, 2019 manisha11 312 views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply manisha11 commented Jan 5, 2019 reply Follow Share @arvin 0 votes 0 votes arvin commented Jan 5, 2019 reply Follow Share @manisha11 atleast how many elements??? one or two or three or.............. lets solve using atleast one element.. which means we can have only one element appearing exactly twice or atleast two element appearing twice or three elements(which is not possible) atleast one element appearing twice : select one element which is appearing twice which can be done in n ways.. and from remaining n-1 select any two elements in n-1C2 ways. #ways = n*(n-1C2) atleast two elements appearing exactly twice: means we will select two elements from n in nC2 ways.. #way= nC2 now total number of ways in which this can be done: =n*((n-1)C2) +nC2 =n(n-1)(n+1)/ 2 answer. 0 votes 0 votes manisha11 commented Jan 5, 2019 reply Follow Share soo GOOD!! 0 votes 0 votes Please log in or register to add a comment.