The number of words that can be formed out of | vedclass

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

Question

(C) The word $ARTICLE$ consists of $7$ distinct letters: $A, R, T, I, C, L, E$.There are $3$ vowels $(A, I, E)$ and $4$ consonants $(R, T, C, L)$.In a

Vedclass · Accepted Answer

$144$

Vedclass · Answer

(C) The word $ARTICLE$ consists of $7$ distinct letters: $A, R, T, I, C, L, E$.There are $3$ vowels $(A, I, E)$ and $4$ consonants $(R, T, C, L)$.In a $7$-letter word,the positions are $1, 2, 3, 4, 5, 6, 7$. The even positions are $2, 4, 6$ (total $3$ places).The $3$ vowels must occupy these $3$ even places. The number of ways to arrange $3$ vowels in $3$ places is $^3P_3 = 3! = 6$.The remaining $4$ consonants must occupy the $4$ odd positions $(1, 3, 5, 7)$. The number of ways to arrange $4$ consonants in $4$ places is $^4P_4 = 4! = 24$.Total number of words = $^3P_3 	imes ^4P_4 = 6 	imes 24 = 144$.

The number of words that can be formed out of the letters of the word $ARTICLE$ so that the vowels occupy even places is

Similar Questions

The number of positive integral solutions of $a \cdot b \cdot c = 30$ is

If ${}^n{P_4} : {}^n{P_5} = 1 : 2$,then $n = $

The number of ways of selecting $15$ teams from $15$ men and $15$ women,such that each team consists of a man and a woman,is

$A$ set contains $(2n + 1)$ elements. The number of subsets of the set which contain at most $n$ elements is:

There are $6$ Men and $8$ Women in a club in which a committee of $5$ people has to be made. What will be the number of ways to select $5$ people if at most one man is selected?

Vedclass Test Series

Exam Paper Generator

Online Exam Module