Respuesta :
Answer:
7
Step-by-step explanation:
There are a total of 7! (7 factorial) possible 7 length strings of the first seven letters of the alphabet that contain no repeated letters. However, we need to consider the restriction that the string must begin or end with a vowel.There are 2 options for the first or last letter (A or E) and 6 options for each of the other 5 letters, for a total of 2 * 6^5 = 30,240 possibilities. However, since the string must begin or end with a vowel, we must also consider the possibility that the string may end with a vowel.There are 2 options for the last letter (A or E) and 6 options for each of the other 6 letters, for a total of 2 * 6^6 = 92,160 possibilities. Since we don't know if the string begins or ends with a vowel, we must add the number of possibilities for each case to get the total number of possibilities.30,240 + 92,160 = 122,400 So the total number of 7 length strings of the first seven letters of the alphabet that contain no repeated letters and begin or end with a vowel (A or E) is 122,400.
