Number of ways in which 7 people can occupy 6 seats, 3 seats on each side in a first class railway compartment if two specified persons are to be always included and occupy adjacent seats on the same side is `(5!)dotk ,t h e nk` has the value equal to ___________.

The number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is beween two boys, is-

Find the number of ways in which six persons can be seated at a round table, so that all shall not have the same neighbours n any two arrangements.

A number of 18 guests have to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on the other side. Determine the number of ways in which the sitting arrangements can be made.

Eighteen guests have to be seated , half on each side of a ling table . Four particular guests desire to sit on one particular side and three others on the other side . Determine the number of ways in which the sitting arrangements can be made .

In how many ways three girls and nine boys can be seated in two vans, each having numbered seats, 3 in the front and 4 at the back? How many seating arrangements are possible if 3 girls sit together in a back row on adjacent seats?Now, if all the seating arrangements are equally likely, what is the probability of 3 girls sitting together in a back row on adjacent seats?

A class has three teachers, Mr. P , Ms. Q, and Mrs. R and six students A,B,C,D,E,F. Number of ways in which they can be seated in a line of 9 chairs, if between any two teachers there are exactly two students, is k !(18), then value of k is ________.

Column I, Column II The number of five-digit numbers having the product o digit 20 is, p. > 70 A closest has five pairs of shoes. The number of ways in which four shoes can be drawn from it such that there will be no complete pair is, q. <60 Three ladies have each brought their one child for admission to a school. The principal wants to interview the six persons one by one subject to the condition that no mother is interviewed before her child. The number of ways in which interview can be arranged is, r. in (50 ,110) The figures 4, 5, 6, 7, 8 are written in every possible order. The number of numbers greater than 56000 is, s. in (40 ,70)

In a three-storey building, there are four rooms on the ground floor, two on the first and two on the second floor. If the rooms are to be allotted to six persons, one person occupying one room only, the number of ways in which this can be done so that no floor remains empty is a. "^8P_6-2(6!) b. "^8P_6 c. "^8P_5(6!) d. none of these

A class has tree teachers, Mr. X , Ms. Y and Mrs. Z and six students A , B , C , D , E , F Number of ways in which they can be seated in a line of 9 chairs,if between any two teachers there are exactly two students is

PARAGRAPH A There are five students S_1,\ S_2,\ S_3,\ S_4 and S_5 in a music class and for them there are five seats R_1,\ R_2,\ R_3,\ R_4 and R_5 arranged in a row, where initially the seat R_i is allotted to the student S_i ,\ i=1,\ 2,\ 3,\ 4,\ 5 . But, on the examination day, the five students are randomly allotted five seats. For i=1,\ 2,\ 3,\ 4, let T_i denote the event that the students S_i and S_(i+1) do NOT sit adjacent to each other on the day of the examination. Then, the probability of the event T_1nnT_2nnT_3nnT_4 is 1/(15) (b) 1/(10) (c) 7/(60) (d) 1/5