Question

Find the number of ways in which the letters of the word thursday can be arranged such that no words start with t or ends with y

Answer 1

Word Thursday can be arranged in 8! ways = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40320.

There are 7! ways of ordering the word Thursday if the first letter is restricted to T because only the 7 remaining ones are allowed to change.

There are 6! ways of ordering the word Thursday if the first letter is restricted to T and the last letter is restricted to Y.

So, There are 7! - 6! ways that the word Thursday can be arranged such that no words start with t or ends with y.

= 7! - 6!

= 5040 - 720

= 4320.


Hope this helps!

Answer 2

The no. ways in which the letters of the word thursday can be arranged such that no words start with t or ends with y =35280


Hint:
total no. of letter =8
no of ways to fill 1st letter =7(all letters
expect t)
no of ways to fill last letter =7(all letters
expect y)

no of ways to fill 2nd letter =6
no of ways to fill 3rd letter =5
no of ways to fill 4th letter =4
no of ways to fill 5th letter =3
no of ways to fill 6th letter =2
no of ways to fill 7th letter =1

hence total no. of ways =
7×6×5×4×3×2×1×7
=35280