Answer:
Kindly check attached picture
Step-by-step explanation:
Number of alphabets = 26
Number of vowels = 5
Number of strings in word = 7
A)How many words begin with R and end with T
First and last has been filled, positions left to fill : 7 - 2 = 5
26^5 = 11881376
B) How many words begin with A or B
First letter can begin with either A or B
Position left to fill = 7 - 1 = 6
2 options for first letter
2 × (26^6) = 617831552
C.) How many words begin with A or end with B
26^6 + 26^6 - 26^5 = 605950176
D.) How many words begin with A or B and end with A or B
Last and first positions have been filled either with A or B
Positions left to fill = 7-2 = 5
4 × (26^5) = 47525504
E) How many words begin with A or B or end with A or B?
(2 × 26^6 + 2 × 26^6 - 4 × 26^5) = 1188137600
f) How many words begin with a vowel and end with a vowel?
2^5 = 32
g) How many words begin with a vowel or end with a vowel?
(5×26^6) + (5×26^6) - (10×26^5) = 2970344000
h) How many words begin with AAB in some order?
AAB = 3 letters
Positions left to fill = 7 - 3 = 4
3 × 26^4 = 1,370,928
i) How many words have no vowels?
26 - 5 = 21 ; 21^7 = 1801088541
j) How many words have exactly one vowel
Number of words × number of vowels × (number of alphabets - number of vowels) ^ number of positions left to fill
7 × 5 × (21^6) = 3001814235