In a class of n n students (we consider all students as distinct), we want to make k k groups where each group must contain at least 1 student. Let S(n,k) S(n,k) denote the number of ways in which such groups can be formed. Which of the following is/are true? (More than one options may be correct.) S(n+1,k)=kS(n,k)+S(n,k−1) S(n+1,k)=kS(n,k)+S(n,k−1) S(n+1,k+1)=kS(n,k+1)+S(n,k) S(n+1,k+1)=kS(n,k+1)+S(n,k) For n,k>1,S(n,k)=∑ j=1 n−1 (n−1 j )S(j,k−1) n,k>1,S(n,k)=∑j=1n−1(n−1j)S(j,k−1) For n,k>1,S(n,k)=∑ j=1 n−1 (n j )S(j,k−1)