41 In how many ways can the squares of the adjoining figure be filled with the letters of the - Maths - Permutations and Combinations

Question

41 In how many ways can the squares of the adjoining figure be
filled with the letters of the word 'ROHINI' so at each row
contains at least one letter?

Neha Sethi · Accepted Answer

Dear student
The word ROHINI contains 6 letters,but we have 8 squares , if we wantto put 6 letters in the square,this means 2 square will be left
So, number of way of selecting such squares=8C6-2=8!6!×2!-2      nCr=n!r!n-r!=8×7×6!6!×2-2=8×72-2=28-2=26Now the number of ways of arranging 6 given letters in the select squares=6!2!=6×5×4×3×2!2!       Here we have divided by 2! as I is coming twice in ROHINI=7202=360
Regards

41. In how many ways can the squares of the adjoining figure be filled with the letters of the word 'ROHINI' so at each row contains at least one letter?