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

(D) The word '$THERAPY$' consists of $7$ distinct letters: $T, H, E, R, A, P, Y$.There are $2$ vowels $(E, A)$ and $5$ consonants $(T, H, R, P, Y)$.Fi

Vedclass · Accepted Answer

$3600$

Vedclass · Answer

(D) The word '$THERAPY$' consists of $7$ distinct letters: $T, H, E, R, A, P, Y$.There are $2$ vowels $(E, A)$ and $5$ consonants $(T, H, R, P, Y)$.First,calculate the total number of arrangements of all $7$ letters,which is $7! = 5040$.Next,calculate the number of arrangements where the $2$ vowels come together. Treat the $2$ vowels as a single unit. Now we have $5$ consonants + $1$ unit = $6$ entities,which can be arranged in $6!$ ways.The $2$ vowels within the unit can be arranged in $2!$ ways.So,the number of ways the vowels come together is $6! 	imes 2! = 720 	imes 2 = 1440$.The number of ways the vowels never come together is the total arrangements minus the arrangements where they are together:$5040 - 1440 = 3600$.

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

Similar Questions

In how many ways can $5$ sportsmen be selected from a group of $10$?

$A$ test consists of $6$ multiple choice questions,each having $4$ alternative answers of which only one is correct. The number of ways in which a candidate answers all six questions such that exactly four of the answers are correct is:

Find $\sum_{r=1}^{5} C(5, r)$

There are seven candidates for $3$ posts. In how many ways can the posts be filled?

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module