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 [tex]n_1[/tex] are line , [tex]n_2[/tex] are like , [tex]n_3[/tex] are like and so on :
[tex]\dfrac{n!}{n_1!n_2!n_3!....}[/tex]
So , the number of distinct letter arrangements can be made from the letters of the word ‘ABBA’:
[tex]\dfrac{4!}{2!2!}=\dfrac{24}{4}=6[/tex]
When the word starts with A , then we need to arrange remaining three letters(BBA) :
Then , Number of arrangements start with A = [tex]1\times \dfrac{3!}{2!}=3[/tex]
∴ Number of arrangements start with A =3
Similarly ,
Number of arrangements finish with A = [tex]1\times \dfrac{3!}{2!}=3[/tex]
∴ Number of arrangements finish with A =3
