What is the number of arrangements of 10 letters the can be formed the

1.	What is the number of arrangements of 10 letters the can be formed the letter word of ANNELIDOUS, so that all the vowels are not come together?1. (10!/2!) - {(6!/2!) × 5!}2. 10! - (6!× 4!)3. 10! - 6!4. 7! - (6!× 5!)
Answer» Correct Answer - Option 1 : (10!/2!) - {(6!/2!) × 5!} Given: The given word is ANNELIDOUS Calculation: There are 10 letters in ANNELIDOUS in this, there are 5 vowels, that is A, E, I, O andU Assume the (AEIOU) as the single object and the remaining letter or object is 5, now we have 6 objects ⇒ The arrangements of all 6 objects = 6!/2! ⇒ The arrangements of(AEIOU) = 5! ⇒ The number of arrangements all the vowels come together = (6!/2!) × 5! All possible arrangements of 10 letters of wordANNELIDOUS = 10!/2! ⇒ The number of arrangments all the vowels do not come together =All possible arrangements - Number of arrangements all vowels come together ⇒ (10!/2!) - {(6!/2!) × 5!} ∴The number of arrangments all the vowels do not come together is(10!/2!) - {(6!/2!) × 5!}.

What is the number of arrangements of 10 letters the can be formed the letter word of ANNELIDOUS, so that all the vowels are not come together?1. (10!/2!) - {(6!/2!) × 5!}2. 10! - (6!× 4!)3. 10! - 6!4. 7! - (6!× 5!)

Answer» Correct Answer - Option 1 : (10!/2!) - {(6!/2!) × 5!}

Given:

The given word is ANNELIDOUS

Calculation:

There are 10 letters in ANNELIDOUS in this, there are 5 vowels, that is A, E, I, O andU

Assume the (AEIOU) as the single object and the remaining letter or object is 5, now we have 6 objects

⇒ The arrangements of all 6 objects = 6!/2!

⇒ The arrangements of(AEIOU) = 5!

⇒ The number of arrangements all the vowels come together = (6!/2!) × 5!

All possible arrangements of 10 letters of wordANNELIDOUS = 10!/2!

⇒ The number of arrangments all the vowels do not come together =All possible arrangements - Number of arrangements all vowels come together

⇒ (10!/2!) - {(6!/2!) × 5!}

∴The number of arrangments all the vowels do not come together is(10!/2!) - {(6!/2!) × 5!}.