Number of  ways can the 13 letters ABCDEFGHXXXYY be arranged in a row so that every Y lies between two X's (not necessarily adjacent) is $K\times 8!{\times }^{\text{13}}{\text{C}}_{\text{5}}$ then k is

There are three major ways  $XXYYX,XYYXX,\text{ and XYXYX}$
or Number of ways to select 5 positions  among 13 in ${ }^{13}{C}_5$ ways in the selected places $XXYYX,XYYXX,\text{ and XYXYX}$

can be arranged in 3  ways. in the remaining 8 places remaining 8 letters can be arranged in 8! ways.

No.of arrangements is  $3\left({ }^{13}{C}_5\right)8!$