1. Tardigrade
  2. Question
  3. Mathematics
  4. 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

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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

Permutations and Combinations

Solution:

(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 $3 \cdot(3 !) 6 !=(18) 6 ! \Rightarrow k=18$