Consider the permutations of the eight letters of the word ``POSITION''. (1) The number of permutations in which the two I's are adjacent and the two O's also are adjacent is $\mathbf { A B C }$. (2) The number of permutations such that the permutations both begin and end with the letter I and furthermore the two O's are adjacent is $\mathbf{DEF}$. (3) The number of permutations that both begin and end with the letter I is $\mathbf{GHI}$. (4) The number of permutations of the 4 letters I, I, O, O is $\mathbf { J }$. Also, the number of permutations of the 4 letters $\mathrm { N } , \mathrm { P } , \mathrm { S } , \mathrm { T }$ is $\mathbf { K L }$. Hence the number of permutations of POSITION which begin or end with either I or O, and furthermore in which none of letters $\mathrm { N } , \mathrm { P } , \mathrm { S } , \mathrm { T }$ are adjacent to each other is $\mathbf{MNO}$.
Consider the permutations of the eight letters of the word ``POSITION''.\\
(1) The number of permutations in which the two I's are adjacent and the two O's also are adjacent is $\mathbf { A B C }$.\\
(2) The number of permutations such that the permutations both begin and end with the letter I and furthermore the two O's are adjacent is $\mathbf{DEF}$.\\
(3) The number of permutations that both begin and end with the letter I is $\mathbf{GHI}$.\\
(4) The number of permutations of the 4 letters I, I, O, O is $\mathbf { J }$. Also, the number of permutations of the 4 letters $\mathrm { N } , \mathrm { P } , \mathrm { S } , \mathrm { T }$ is $\mathbf { K L }$.
Hence the number of permutations of POSITION which begin or end with either I or O, and furthermore in which none of letters $\mathrm { N } , \mathrm { P } , \mathrm { S } , \mathrm { T }$ are adjacent to each other is $\mathbf{MNO}$.