∵ Total number of ways in which train has stopped at exactly 5 stations =‌15C5 And total number of ways in which train has not stopped in consecutive stations x1+x2+x3+x4+x5+L=15−4=11 xi= number of station left before i‌th ‌ station x1≥0x2,x3,x4,x5≥1, and L= station left after 4 stations x1+(x2−1)+(x3−1)+(x4−1)+(x5−1)+L =11−4=7 ∴‌ Total number of solution ‌‌=‌7+5−1C6−1 ‌=‌11C5 ∴ Required ways =‌15C5−‌11C5
