• # question_answer There are three girls in a class of 10 students. The number of different ways in which they can be seated in a row such that no two of the three girls are together is A) $7\ !\ {{\times }^{6}}{{P}_{3}}$ B) $7\ !\ {{\times }^{8}}{{P}_{3}}$ C) $7\ !\ \times 3\ !$ D) $\frac{10\ !}{3\ !\ 7\ !}$

Seven boys can be seated in a row in $7\ !$ ways. Hence the total no. of arrangement such that no two girls seated together$=7\ !\ {{\times }^{8}}{{P}_{3}}$.