Let `P_n` denotes the number of ways in which three people can be selected out of 'n' people sitting in a row, if no two of them are consecutive. If `P_(n+1)- P_n=15` then the value of 'n` is____.

If "^(2n+1)P_(n-1):^(2n-1)P_n=3:5, then find the value of n .

Given that n is the odd the number of ways in which three numbers in A.P. can be selected from {1,2,3,4….,n} is

if n objects are arranged in a row then the number of ways of selecting three of these objects so that no two of them are next to each other is

P(n):11^(n+2)+1^(2n+1) where n is a positive integer If P(n) = 14642, then the value of n is -

The number of three-digit numbers having only two consecutive digit identical N , then the value of (N//2)^(1//2) is _______.

Let T_n denote of the number of triangles which can be formed using the vertices of a regular polygon of n sides If T_(n+1)-T_n=21 then n is

Let X denote the number of times heads occur in n tosses of a fair coin. If P(X=4),\ P(X=5)\ a n d\ P(X=6) are in AP; the value of n is

Let T_(n) denote the number of triangles which can be formed using the vertices of a regular polygon of n sides . If T_(n+1)-T_(n)=21 then find the values of n .

If N is the number of ways in which 3 distinct numbers canbe selected from the set {3^1,3^2,3^3, ,3^(10)} so that they form a G.P. then the value of N//5 is ______.

Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number in which 5 boys and 5 girls stand in such a way that exactly four girls stand consecutively in the queue. Then the value of m/n is ____