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(6!) then the value of k is

Question

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(6!) then the value of k is (A) 18 (B) 12 (C) 24 (D) 6

Tardigrade Admin · Accepted Answer

(i) T S S T S S T S S (ii) S T S S T S S T S (iii) S S T S S T S S T Hence 3 ⋅(3 !) 6 !=(18) 6 ! ⇒ k=18

Q. 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 $k (6!)$ then the value of $k$ is

18

12

24

6

(i) T S S T S S T S S
(ii) S T S S T S S T S
(iii) S S T S S T S S T
Hence $3 \cdot (3!) 6! = (18) 6! \Rightarrow k = 18$

Q. 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(6!) then the value of k is

18

12

24

6

(i) T S S T S S T S S (ii) S T S S T S S T S (iii) S S T S S T S S T Hence 3⋅(3!)6!=(18)6!⇒k=18

Q. 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 $k (6!)$ then the value of $k$ is

(i) T S S T S S T S S
(ii) S T S S T S S T S
(iii) S S T S S T S S T
Hence $3 \cdot (3!) 6! = (18) 6! \Rightarrow k = 18$