Aptitude - Permutation and Combination - Discussion

In this question won't the arrangement of non vowels matter and why?

If there is another vowel 'o' what should be done like in 'outstanding' here a, i, o, u are vowels do we have to consider (aiou) = 1 letter for calculation?

In how many ways LEADING be arranged such a way that atleast two vowels always together?

Hi if two vowels are repeated in same word then will you take it as same or as different?

In some cases unit's place, tens place's and hundred's place are used what its mean?

All the consonants can also be written as a unit?

@Tom and @Shantha.

Whenever there is a reference to some arrangement it is permutation. Whenever there is a reference to some selection it is combination.

The given question requires us to find the number of ways in which the word LEADING can be arranged with the condition that the vowels (EAI) always be together. Thus we need to apply the concept of permutation.

Here, since the vowels EAI must always be together we consider it as a single word (EAI).

Thus, LDNG (EAI) make a 5 letter word.

It can be arranged in 5p5 ways = 5!ways.

Now, since EAI can arrange itself in 3p3 or 3! ways, the word LDNG (EAI).

Can thus be arranged or PERMUTED in 3!*5! ways = 720 ways.

In what situations we can permutation or combination?

Then how we won't take E+A+I+(LDNG) = 4.

Hi friends.

We know that formula n!=n (n-1) (n-2).....3.2.1. Suppose there n way to choose first element (since there are n elements).

After that there are n-1 ways to choose second element because already we choose one element from n elements that's why we are assuming this way. Similarly n-2 ways to chose the third element..etc it's going like this.

n!=n (n-1).

n!=n (n-1) (n-2) if n>2 or equals 2.

n!=n (n-1) (n-2) (n-3) if n>3 or equals 3.

Hope you understood.