Permutation or combination?

There are 3 choices for the first letter and 3 choices for the last.

Since there are 3 letters in between the first and last, and since

we must have at least 2 vowels, the middle 3 letters can follow

the following patterns, (V for vowel and C for consonant):

(i) C,V,V

(ii) V,C,V

(iii) V,V,C

(iv) V,V,V

Now for case (i), the consonant must be the same as the first

letter, and since the 2 vowels must be different there are just

2 possible arrangements of the 2 vowels available. This gives

us a total of 3*2*3 = 18 possible permutations in this case,

i.e., 3 choices for the first letter, 2 choices for the first vowel

and 3 choices for the last letter.

For case (ii), there are 2 choices for the first vowel, 3 for the

middle consonant and 2 choices for the second vowel. This

gives us 3*2*3*2*3 = 108 possible permutations in this case.

Case (iii) is the mirror image of case (i) so we get 18 more

possible permutations in this case.

For case (iv) once the first vowel is chosen the second vowel

must be the other possible vowel and the third vowel must

be the same as the first. Thus there are 3*2*3 = 18 more

possible permutations in this case.

The total number of permutations is thus 108 + 3*18 = 162.

General rule - When the order of alphabets/things is important or creates a different result, then you need to use Permutation, other wise Combination.

Example - If BA and AB are same in a example, then use Combination.

Above Example has several conditions on each alphabet, so it will be combination.

Combination

combination