If H _ , denotes the number of ways in which n horses participating in a race can reach the finishing line. when one or more horses can reaci the finishing line at the same time. Then

Step-by-step solution

The sequence of two horses reaching the finishing line can be 2 or 1+1 Number of ways =1+2!=3 The sequence of three horses reaching the finishing line and number of ways are shown below 3 1 way 2+1 ^3 C₂=3 ways 1+2 ^3 C₁=3 ways 1+1+1 3!=6 Hence. H ₃=1+3+3+6=13 The sequence of four horses reading the finishing line and number of ways are shown below aligned & 4 1 ways & 3+1 ^4 C ₃ ways & 1+3 ^4 C ₁ ways & 2+2 ^4 C ₂ & 2+1+1 aligned ( 4! 2!1!1!2! ) 3! ways 1+1+1+1 4! ways Hence. H ₄=1+4+4+6+36+24=75