In how many different ways can the letters of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The word '$DETAIL$' consists of $6$ letters: $3$ vowels $(A, E, I)$ and $3$ consonants $(D, T, L)$.There are $6$ positions in total: $1, 2, 3, 4,

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(C) The word '$DETAIL$' consists of $6$ letters: $3$ vowels $(A, E, I)$ and $3$ consonants $(D, T, L)$.There are $6$ positions in total: $1, 2, 3, 4, 5, 6$.The odd positions are $1, 3,$ and $5$ (total $3$ positions).The even positions are $2, 4,$ and $6$ (total $3$ positions).We need to place $3$ vowels in $3$ odd positions,which can be done in $3! = 6$ ways.We need to place $3$ consonants in $3$ even positions,which can be done in $3! = 6$ ways.Therefore,the total number of arrangements is $6 	imes 6 = 36$.

In how many different ways can the letters of the word '$DETAIL$' be arranged in such a way that the vowels occupy only the odd positions?

Similar Questions

How many different words can be formed with the letters of the word '$BHARAT$'? In how many of these are $B$ and $H$ never together?

In how many different ways can the letters of the word '$KURUKSHETRA$' be arranged?

How many different four-letter words can be formed (the words need not be meaningful) using the letters of the word $MEDITERRANEAN$ such that the first letter is $E$ and the last letter is $R$?

The total number of $4$-digit numbers which can be formed using the digits $1, 2, 3, 4$ without repetition such that the digit $n+1$ never immediately follows the digit $n$ (for $n=1, 2, 3$) is:

The solution set of $^{10}C_{x-1} > 2 \cdot ^{10}C_x$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module