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 ________.

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

There are 6 students A,B,C,D,E,F. In how many ways can they be seated in a line so that C and D do not sit together?

Number of ways in which 4 students can sit in 7 chair in a row, if there is no empty chair between any two students is :

A team of four students is to be selected from a total of 12 students. The total number of ways in which the team can be selected such that two particular students refuse to be together and other two particular students wish to be together only is equal to a. 220 b. 182 c. 226 d. none of these

Let m denotes the number of ways in which 5 boys and 5 girls can be arranged in a line alternately and n denotes the number of ways in which 5 boys and 5 girls an be arranged in a circle so that no two boys are together . If m= kn then the value of k is :

Number of integral values of k for which the equation 4 cos^(-1)(-|x|)=k has exactly two solutions, is: (a) 4 (b) 5 (c) 6 (d) 7

Number iof ways in which m men and n women can be arranged in a rwo so that no two women are together is m!^(m=1)P_n Also number oif ways in which m men and n women can be seated in a row so that all the n women are together is (m=1)!n! On the basis of above informatiion answer the following question: Number of ways in which 10 boys and 5 girls can be seated in a row so that no boy sits between girls is (A) 5!xx10_P_5 (B) 5!xx11_P_5 (C) 10!xx11_P_5 (D) 5!xx11

Number iof ways in which m men and n women can be arranged in a rwo so that no two women are together is m!^(m=1)P_n Also number oif ways in which m men and n women can be seated in a row so that all the n women are together is (m=1)!n! On the basis of above informatiion answer the following question: Therre are 10 intermediate stations between two places P and Q. the number of ways in 10 boys &5 girls can be seated in a row so that no boy sits between girls

The number of values of k for which the equation x^3-3x+k=0 has two distinct roots lying in the interval (0,1) is (a) three (b) two (c) infinitely many (d) zero

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 ___________.