`n_1a n dn_2` are four-digit numbers, find the total number of ways of forming `n_1a n dn_2` so that `n_2` can be subtracted from `n_1` without borrowing at any stage.

If n_1 and n_2 are five-digit numbers, find the total number of ways of forming n_1 and n_2 so that these numbers can be added without carrying at any stage.

Find the total number of integer n such that 2lt=nlt=2000 and H.C.F. of n and 36 is 1.

Find the total number of n -digit number (n >1) having property that no two consecutive digits are same.

Find the number of ways in which n different prizes can be distributed among m(< n) persons if each is entitled to receive at most n-1 prizes.

Which of the following is not the number of ways of selecting n objects from 2n objects of which n objects are identical

Two players P_1a n dP_2 play a series of 2n games. Each game can result in either a win or a loss for P_1dot the total number of ways in which P_1 can win the series of these games is equal to a. 1/2(2^(2n)-^ "^(2n)C_n) b. 1/2(2^(2n)-2xx^"^(2n)C_n) c. 1/2(2^n-^"^(2n)C_n) d. 1/2(2^n-2xx^"^(2n)C_n)

Find the number of subsets of A if A = { X : X = 4n +1, 2 lt= n lt= 5, n in NN }

Let N denote the number of days. If the value of N! is equal to the total number of hours in N days then find the value of N?