The number of letters in word "ALGORITHM" = 9
The number of combinations to select r things from n things is given by :-
[tex]C(n,r)=\dfrac{n!}{r!(n-r)!}[/tex]
Now, the number of combinations to select 6 letters from 9 letters will be :-
[tex]C(9,8)=\dfrac{9!}{6!(9-6)!}=\dfrac{9\times8\times7\times6!}{6!\times3!}=84[/tex]
Thus , the number of ways can six of the letters of the word ALGORITHM=84
The number of ways to arrange n things in a row :[tex]n![/tex]
So, the number of ways can the letters of the word ALGORITHM be arranged in a be seated together in the row :-
[tex]9!=362880[/tex]
If GOR comes together, then we consider it as one letter, then the total number of letters will be = 1+6=7
Number of ways to arrange 9 letters if "GOR" comes together :-
[tex]7!=5040[/tex]
Thus, the number of ways to arrange 9 letters if "GOR" comes together=5040
