The number of four-letter words that can be f | vedclass

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

Question

(B) The word '$MAYANK$' consists of $6$ letters: $M, A, Y, A, N, K$. The distinct letters are ${M, Y, N, K}$ and the repeated letter is ${A, A}$.To fo

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(B) The word '$MAYANK$' consists of $6$ letters: $M, A, Y, A, N, K$. The distinct letters are ${M, Y, N, K}$ and the repeated letter is ${A, A}$.To form a $4$-letter word containing both '$A$'s,we need to select $2$ more letters from the remaining $4$ distinct letters ${M, Y, N, K}$.The number of ways to select $2$ letters from $4$ is $^4C_2 = 6$.Now,we have $4$ letters in total (e.g.,$A, A, X, Y$). The number of ways to arrange these $4$ letters is $\frac{4!}{2!} = 12$.Total words containing both '$A$'s = $6 	imes 12 = 72$.Now,we calculate the number of words where both '$A$'s are together. Treat $(AA)$ as one unit. We have $3$ units to arrange: $(AA), X, Y$. The number of ways to arrange these is $3! = 6$.Since we have $6$ pairs of letters ${X, Y}$,the number of words where both '$A$'s are together is $6 	imes 6 = 36$.The number of words where both '$A$'s are $NOT$ together = (Total words with both '$A$'s) - (Words with '$A$'s together) = $72 - 36 = 36$.

The number of four-letter words that can be formed from the letters of the word '$MAYANK$' such that both '$A$'s are included but never together is equal to:

Similar Questions

In how many different ways can the letters of the word '$THERAPY$' be arranged so that the vowels never come together?

In how many ways can a committee consisting of one or more members be formed out of $12$ members of the Municipal Corporation?

Everybody in a room shakes hands with everybody else. The total number of handshakes is $66$. The total number of persons in the room is:

In how many ways can a committee,consisting of $5$ men and $6$ women,be formed from $8$ men and $10$ women?

In how many different ways can the letters of the word '$OPTICAL$' be arranged so that the vowels always come together?

Vedclass Test Series

Exam Paper Generator

Online Exam Module