In how many ways can the letters of word TOUKIR be arranged so that th

1.	In how many ways can the letters of word TOUKIR be arranged so that the vowels in the word always occur in the dictionary order as we move from left to right?1). 62). 243). 604). 120
Answer» The given WORD is TOUKIR. If vowels are arranged in dictionary order, then I will COME before O and O will come before U. There are 6 letters in this word which need to be arranged. Let’s first ARRANGE the vowels. They can be placed in any 3 of the 6 places. Number of ways of choosing these places = ⁶C₃ There’s only one way of ARRANGING the vowels in the selected places, and that is the alphabetical order. Now, the remaining three letters, i.e. T, K and R are to be placed in remaining 3 places. This can be done in 3! Ways. ∴ Total number of POSSIBLE arrangements = ⁶C₃× 3! = 6 × 5 × 4 = 120

In how many ways can the letters of word TOUKIR be arranged so that the vowels in the word always occur in the dictionary order as we move from left to right?1). 62). 243). 604). 120

Answer»

The given WORD is TOUKIR. If vowels are arranged in dictionary order, then I will COME before O and O will come before U.

There are 6 letters in this word which need to be arranged.

Let’s first ARRANGE the vowels. They can be placed in any 3 of the 6 places.

Number of ways of choosing these places = ⁶C₃

There’s only one way of ARRANGING the vowels in the selected places, and that is the alphabetical order.

Now, the remaining three letters, i.e. T, K and R are to be placed in remaining 3 places. This can be done in 3! Ways.

∴ Total number of POSSIBLE arrangements = ⁶C₃× 3! = 6 × 5 × 4 = 120