In what ways the letters of the word puzzle can be arranged to from the different new words so that the vowels always come together?

What are the different ways in which letters of the word "PARROT" can be arranged in such a way that the vowels always come together?

  1. 120 ways
  2. 230 ways 
  3. 320 ways 
  4. 210 ways
  5. 250 ways

Answer (Detailed Solution Below)

Option 1 : 120 ways

Given:

A word "PARROT" with has 5 letters from which 4 consonants and 2 vowels.

Formula used:

Factorial n! = n × (n - 1) × ..... × 3 × 2 × 1

Calculation:

The arrangement is made in such a way that the vowels always come together. 

⇒ "PRRT(AO)"

Considering vowels as one letter, 5 different letters can be arranged in 5! ways.

We have two "R" also = 5!/2!

⇒ 5!/2! = 60 ways 

The vowels "AO" can be arranged themselves in 2! ways.

⇒ 2! = ways 

Required number of ways = 60 × 2 = 120 ways.

∴ "PARROT" can be arranged in such a way that the vowels always come together for that we have 120 ways.

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11. 

In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

Answer: Option A

Explanation:

Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) =
7 x 6 x 3
= 63.
2 x 1


12. 

How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?

Answer: Option C

Explanation:

'LOGARITHMS' contains 10 different letters.

Required number of words = Number of arrangements of 10 letters, taking 4 at a time.
= 10P4
= (10 x 9 x 8 x 7)
= 5040.


13. 

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

A. 10080
B. 4989600
C. 120960
D. None of these

Answer: Option C

Explanation:

In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.

Thus, we have MTHMTCS (AEAI).

Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.

Number of ways of arranging these letters =
8! = 10080.
(2!)(2!)

Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.

Number of ways of arranging these letters = 4! = 12.
2!

Required number of words = (10080 x 12) = 120960.

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1. 

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

Answer: Option D

Explanation:

We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).


2. 

In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?

Answer: Option C

Explanation:

The word 'LEADING' has 7 different letters.

When the vowels EAI are always together, they can be supposed to form one letter.

Then, we have to arrange the letters LNDG (EAI).

Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.

The vowels (EAI) can be arranged among themselves in 3! = 6 ways.

Required number of ways = (120 x 6) = 720.

Video Explanation: https://youtu.be/WCEF3iW3H2c

In what ways the letters of the word puzzle can be arranged to form the different new words?

2) In what ways the letters of the word "PUZZLE" can be arranged to form the different new words so that the vowels always come together? Answer with the explanation: The word PUZZLE has 6 different letters. As per the question, the vowels should always come together.

How many different ways can letter be arranged so that the vowels always come together?

The number of ways the word TRAINER can be arranged so that the vowels always come together are 360.

In what ways the letters of the word actors can arrange so that the vowels occupy only the even positions?

Q. 3. In what ways the letters of the word ACTORS can arrange so that the vowels occupy only the even positions? ATQ, the vowels A, O can be placed at any of the position out of 2, 4, and 6.

How many different ways can the letters of the word letter be arranged?

=360 the number of ways.