Question

In how many different ways can the letters of the word 'leading' be arranged in such a way that the vowels always come together? 360 480 720 5040

Answer 1

Answer:

So the given word is ' leading '.

We have to see the arrangements so that the vowels are together .

Number of letters in 'leading' is 7 .

Number of vowels in 'leading' is 3 .

Ways to create consecutive place

There are 5 ways of choosing a number so that there will be consecutive places .

Ways to create vowels

Now we will concentrate on the vowels .

There are 3 vowels that can be arranged in any way .

For the first choice there are 3 chances .

Then there are 2 chances .

Then there is 1 chance for the last remaining one .

So the vowels can be arranged in 3 × 2 × 1 = 6 ways .

Ways to create consonants

There are 4 consonants .

For the first consonant there will be 4 choices .

For the second ..... 3 choices and so on ...

Number of ways will be 4 × 3 × ... 1 = 24

Total ways

According to the Principle of counting :

Total number of choices will be = 24 × 6 × 5

⇒ 144 × 5

⇒ 720

So OPTION - 720 is correct .

Although everyone knows :

Ways to arrange n number of items = n! such that :

n! = 1 × 2 × .... n .

This is called factorial .

Answer 2

Question:

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

(a) 360

(b) 480

(c) 720

(c) 5040

Answer:

The correct answer is option (c) 720.

Step-by-step explanation:

The word 'leading' has 7 different letters.

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

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

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

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

The required number of ways $= (120 * 6) = 720$.

Therefore, the correct answer is option (c) 720.

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