a) How many permutations are there of the letters in the word baseball?
my thinking $\displaystyle \frac{8}{2!2!2!}=5040$
b) How many begin with the letter a?
c) How many end with the letter e?
Hello, William!
a) How many permutations are there of the letters in the word BASEBALL?
My thinking: $\displaystyle \frac{8}{2!2!2!}\:=\:5040$ . . . . Right!
b) How many begin with the letter A?
Place one of the $\displaystyle A$'s in front: .$\displaystyle A\:\_\:\_\:\_\:\_\:\_\:\_\:\_$
Then the other seven letters $\displaystyle \{A,B,B,E,L,L,S\}$
. . can be arranged in $\displaystyle \frac{7!}{2!2!} \:=\:1260$ ways.
c) How many end with the letter E?
Place the $\displaystyle E$ on the end: .$\displaystyle \_\:\_\:\_\:\_\:\_\:\_\:\_\:E$
Then the other seven letters $\displaystyle \{A,A,B,B,L,L,S\}$
. . can be arranged in $\displaystyle \frac{7!}{2!2!2!} \:=\:630$ ways.