14 The number of ways to arrange 5 boys and 6 girls in a row such that girls can be adjacent to other girls but boys cannot be adjacent to other boys is $6!\times k$. Find the value of $k$.
14 Answer: (2520)
First we arrange the 6 girls in 6 ! ways. Next, there are 7 spaces between the 6 girls to insert the 5 boys. Hence $k={ }^{7} \mathrm{C}_{5} \times 5!=2520$.