A team of 11 is picked from 15 players, who include Kiran and Joseph…

Step 1. Both play. Choose $9$ more from the other $13$: $^{13}C_{9} = {}^{13}C_{4} = 715$.

Step 2. Neither plays. Choose all $11$ from the other $13$: $^{13}C_{11} = {}^{13}C_{2} = 78$.

Step 3. Exactly one. Pick which one in $2$ ways, then $10$ more from $13$: $2 \times {}^{13}C_{10} = 2 \times 286 = 572$.

Step 4. Check. $715 + 78 + 572 = 1365 = {}^{15}C_{11}$, every team.