The number of ways in which 12 people may be divided into three sets of equal size is

The number of ways can five people be divided into three groups is

The number of ways in which 10 people can be assigned to two triple and two double rooms is

The number of ways in which 19 different objects can be divided into two groups of 13 and 6 is

The number of ways in which a 7 people can sit around a round table is

The number of ways in which 21 objects can be grouped into three groups 8, 7 and 6 object is

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____.

Number of ways in which 200 people can be divided in 100 couples is a. ((200)!)/(2^(100)(100 !)) b. 1xx3xx5xxxx199 c. ((101)/2)""((102)/2)"".............((200)/2) d. ((200)!)/((100)!)

A shelf contains 20 books of which 4 are single volume and the other form sets of 8, 5, and 3 volumes. Find the number of ways in which the books may be arranged on the shelf so that volumes of each set will not be separated. (ii)volumes of each set remain in their due order.

Statement 1: Number of ways in which 30 can be partitioned into three unequal parts, each part being a natural number is 61. Statement 2; Number of ways of distributing 30 identical objects in three different boxes is ^30 C_2dot

Statement 1: The number of positive integral solutions of a b c=30 is 27. Statement 2: Number of ways in which three prizes can be distributed among three persons is 3^3