m men and n women are to be seated in a row that no two women sit together . If m gt n, then show that the mumber of ways in which they can be sated is `(m!(m+1)!)/((m-n+1)!)`

m men and n women are to be seated in a row so that no two women sit together. If (m>n) then show that the number of ways in which they can be seated as (m!(m+1)!)/((m-n+1)!) .

There are n seats round a table marked 1,2,3,…..n the number of ways in which m(len) persons can take seats is

If A.M. and G.M. between two numbers is in the ratio m : n then prove that the numbers are in the ratio (m+sqrt(m^2-n^2)):(m-sqrt(m^2-n^2))dot

For 2 positive numbers m and n, which is the correct relation for (m+n) (1/m + 1/n)?

Find the number of ways in which 6 men and 5 women can dine at around table if no two women are to sit so together.

The ratio of the sums of m and n terms of an A.P. is m^2 : n^2. Show that the ratio of m^(th) and n^(th) term is (2m-1) : (2n -1) .

The ratio of the sum of m and n terms of an A.P. is m^(2) :n^(2) . Show that the ratio mth and nth term is (2m-1) : (2n-1).

A coin is tossed (m + n) times (m gtn). Show that the probability of at least m consecutive heads is (n+2)//2^(m+2).

Let T_(r) be the rth term of an A.P. If m. T_(m) = n.T_(n) , the show that, T_(m+n) = 0 .

There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by 84, then the value of m is