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

Step-by-step 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 :

$\dfrac{n!}{n_1!n_2!n_3!....}$

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

$\dfrac{4!}{2!2!}=\dfrac{24}{4}=6$

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

Then , Number of arrangements start with A = $1\times \dfrac{3!}{2!}=3$

∴ Number of arrangements start with A =3

Similarly ,

 Number of arrangements  finish with A = $1\times \dfrac{3!}{2!}=3$

∴ Number of arrangements  finish with A =3