Question

How many distinct letter arrangements can be made from the letters of the word ‘ABBA’ ? How many arrangements start with A ? How many of these arrangements finish with A ?

Answer 1

Answer: Number of distinct letter arrangements can be made from the letters of the word ‘ABBA’: =6

Number of arrangements start with A= 3

Number of arrangements finish with A =3

Explanation:

Given word : ABBA

Total letters = 4

Number of A's = 2

Number of B's = 2

Number of ways to arrange n letters such that
`n_1` are line ,
`n_2` are like ,
`n_3` are like and so on :

`(n!)/(n_1!n_2!n_3!....)`

So , the number of distinct letter arrangements can be made from the letters of the word ‘ABBA’:

`(4!)/(2!2!)=(24)/(4)=6`

When the word starts with A , then we need to arrange remaining three letters(BBA) :

Then , Number of arrangements start with A =
`1* (3!)/(2!)=3`

∴ Number of arrangements start with A =3

Similarly ,

Number of arrangements finish with A =
`1* (3!)/(2!)=3`

∴ Number of arrangements finish with A =3