SHAIK AASIF AHAMED
Last Activity: 10 Years ago
Hello student,
Please find the answer to your question below
There are 9 letters so there are 7 cases
case 1: i _ _ _ _ _ _ _ i
here no of ways =7!/2!
i _ _ _ _ _ _ i_
no of ways=6*6!/2!
i _ _ _ _ _ i _ _
no of ways=6*5*5!/2!
similarly we will different ways get as i moves forward every time by one position as
6*5*4*4!/2! , 6*5*4*3*3!/2! ,6*5*4*3*2*2!/2! ,6*5*4*3*2*1!/2! till the case ini_ _ _ _ _ _ occurs
case 2:_i _ _ _ _ _ _ i
by writing ways similarly as above we get
6*6!/2!,6*5*5!/2!,6*5*4*4!/2! , 6*5*4*3*3!/2! ,6*5*4*3*2*2!/2! ,6*5*4*3*2*1!/2! till the case _ini _ _ _ _ _ occurs
case3:_ _i_ _ _ _ _ i
by writing ways similarly as above we get
6*5*5!/2!,6*5*4*4!/2! , 6*5*4*3*3!/2! ,6*5*4*3*2*2!/2! ,6*5*4*3*2*1!/2! till the case_ _ini _ _ _ _ occurs
case 4:_ _ _i _ _ _ _ i
by writing ways similarly as above we get
6*5*4*4!/2! , 6*5*4*3*3!/2! ,6*5*4*3*2*2!/2! ,6*5*4*3*2*1!/2! till the case_ _ _ini_ _ _ occurs
case 5:_ _ _ _i _ _ _ i
by writing ways similarly as above we get
6*5*4*3*3!/2! ,6*5*4*3*2*2!/2! ,6*5*4*3*2*1!/2! till the case_ _ _ _ ini _ _ occurs
case 6:_ _ _ _ _i _ _ i
by writing ways similarly as above we get
6*5*4*3*2*2!/2! ,6*5*4*3*2*1!/2! till the case_ _ _ _ _ini_ occurs
case 7:_ _ _ _ _ _i ni
by writing ways similarly as above we get
6*5*4*3*2*1!/2! till the case_ _ _ _ _ _ini occurs
By adding all the above cases we get
(7*6!/2!)+(2*6*6!/2!)+(5*3*6!/2!)+(4*4*6!/2!)+(3*5*6!/2!)+(2*6*6!/2!)+(7*6!/2!)=84*6!/2=9!/12
hence the value of k=9