11. Determine the number of different arrangements of the six letters in the word ANSWER
a) Without restrictions
b) that begin with an $\mathrm{S}$
c) That begin with a vowel and end with a consonant
d) That have the three letters A, N, and S adjacent and in the order ANS
e) That have the three letters A, N, and S adjacent, but not necessarily in that order
Answer
The number of different arrangements of the six letters in the word ANSWER without any restrictions is \(\boxed{720}\).
Step 1 ：Determine the number of different arrangements of the six letters in the word ANSWER without any restrictions.
Step 2 ：Since there are no repeating letters, we can simply calculate the factorial of the number of letters, which is 6.
Step 3 ：Calculate the factorial of 6 to get the total number of arrangements.
Step 4 ：\(6! = 720\)
Step 5 ：The number of different arrangements of the six letters in the word ANSWER without any restrictions is \(\boxed{720}\).
