The least value of the natural number n satisfying C(n, 5)+C(n, 6)>C(n+1,5) is

Step-by-step solution

aligned & We have, ^n C₅+ ^n C₆> ^ n+1 C₅ & ^ n+1 C₆> ^ n+1 C₅ & (n+1) ! 6 !(n+1-6) ! > (n+1) ! 5 !(n+1-5) ! & 5 !(n-4) !>6 !(n-5) ! & 5 !(n-4)(n-5) !>6 5 !(n-5) ! & n-4>6 & n>10 & n=11 & aligned