Bissoy.com
Doctors Medicines MCQs Q&A

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

In how many different ways can the letters of the word 'THERAPY' be arranged so that the vowels never come together? Correct Answer 3600

Given word is THERAPY.

Number of letters in the given word = 7

These 7 letters can be arranged in 7! ways.

Number of vowels in the given word = 2 (E, A)

The number of ways of arrangement in which vowels come together is 6! x 2! ways

 

Hence, the required number of ways can the letters of the word 'THERAPY' be arranged so that the vowels never come together = 7! - (6! x 2!) ways = 5040 - 1440 = 3600 ways.

 

Related Questions

Questions below followed by three quantities. Find the relationship between them. Quantity I: In how many ways the letter of the word ‘MANUAL’ can be arranged so that vowels come together? Quantity II: Find the number of ways of forming a five number Team for a project from a group of 6 workers and 5 managers such that no odd numbers of managers are selected in the project? Quantity III: The letters of the word NATURE are to be arranged so that three vowels should not come together. Find the number of arrangement.
The following question has three statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. An 8-letter word has no repetitive letter. Find the number of vowels in the word. I) No. of ways in which the consonants can be arranged is 720. II) No. of ways in which the vowels can be arranged is 2. III) 10080 different words can be formed keeping the vowels together.
In the following question, two statements are numbered as I and II. On solving these statements, we get quantities I and II respectively. Solve for the both quantities and choose the correct option. Quantity I – In how many ways letters of MOBILE can be arranged when vowels are always together. Quantity II – In how many ways letters of MONDAY can be arranged when vowels are not together.
Which of the following statements about gene therapy are correct?
P. Affected individuals, but not their progeny, can be cured through germline gene therapy.
Q. Affected individuals, as well as their progeny, can be cured through germline gene therapy.
R. Affected individuals, but not their progeny, can be cured through somatic gene therapy.
S. Affected individuals, as well as their progeny, can be cured through somatic gene therapy.
In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option. Quantity A: In how many ways can the word ‘DISTURBANCE’ be arranged such that all the consonants are always together? Quantity B: In how many ways can the word ‘DISTURBANCE’ be arranged such that all the vowels are always together?
In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and chose the correct option. Quantity A: In how many different ways can the letters of the word JUMBLE be arranged? Quantity B: In how many different ways can the letters of the word BOTTLE  be arranged?
In how many different ways can the letters of the word ‘THERAPIST’ be arranged so that the vowels never come together?
If in the word ‘DIPLOMACY’, all the vowels are first arranged alphabetically and then all the consonants are arranged alphabetically and then all the vowels are replaced by the next letters of the English alphabet and the consonants are replaced by the previous letters from the English alphabet, which letter will be the sixth from the right end in the new word thus obtained?
City High School must put together a debating team consisting of four debaters.There are candidates of equal ability : X,Y and Z who are all seniors; and A,B,C and D who are all juniors..The school requires that there should be two seniors and two juniors in the team.It is also necessary that all of the debaters be able to work with one another. *Debaters Y and A cannot work together. *Debaters Z and C cannot work together. *Debaters A and B cannot work together. which of the following statements must be false? 1.Debaters Y and C are never selected together. 2.Debaters Z and D are never selected together. 3.Debaters Z and D are never selected together.
In how many different ways can the letters of the word EXTRA be arranged so that the vowels are never together?