The number of 4-letter words, with or without | vedclass

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

Question

(D) The word $INCONSEQUENTIAL$ consists of $15$ letters. First, identify the distinct vowels and consonants. Vowels: {$I$, $O$, $E$, $U$, $A$} ($5$ di

Vedclass · Accepted Answer

$3600$

Vedclass · Answer

(D) The word $INCONSEQUENTIAL$ consists of $15$ letters. First, identify the distinct vowels and consonants. Vowels: {$I$, $O$, $E$, $U$, $A$} ($5$ distinct vowels). Consonants: {$N$, $C$, $S$, $Q$, $T$, $L$} ($6$ distinct consonants). We need to select $2$ vowels out of $5$ and $2$ consonants out of $6$. The number of ways to choose these letters is $\binom{5}{2} 	imes \binom{6}{2} = 10 	imes 15 = 150$. Each selection contains $4$ distinct letters, which can be arranged in $4! = 24$ ways. Total number of words = $150 	imes 24 = 3600$.

The number of $4$-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word $INCONSEQUENTIAL$, without repeating any letter, is:

Similar Questions

The number of $4$ letter words that can be formed with the letters in the word $EQUATION$ with at least one letter repeated is

How many $6$-digit numbers can be formed from the digits $0, 1, 3, 5, 7,$ and $9$ which are divisible by $10$,given that no digit is repeated?

Find the number of permutations of the letters of the word $ALLAHABAD$.

In a library,there are $a$ books of type $A$,$2$ books of type $B$,$3$ books of type $C$,and $1$ book of type $D$. In how many ways can these books be arranged?

If the letters of the word $SACHIN$ are arranged in all possible ways and these words are written out as in a dictionary,then the word $SACHIN$ appears at serial number:

Vedclass Test Series

Exam Paper Generator

Online Exam Module