Guys, please answer if you\'re 100% sure. There are NOT homework questions nor a

Question

Guys, please answer if you're 100% sure. There are NOT homework questions nor assignments. I'm preparing for exam after 2 days and these are all old exams questions I want them to be solved so I can compare my answers with yours after I finish studying today.

a. (25 points) How many strings of 8 English letters (English has 26 letters) are there
(i) (5 points) if letters can be repeated?
(ii) (5 points) if no letter can be repeated?
(iii) (5 points) that start with MC and end with ER, where letters can be repeated?
(iv) (5 points) that start with D or end with TION, where no letter can be repeated?
(v) (5 points) that contain the letters in {T, I, O, N}, where letters can be repeated?

Explanation / Answer

a. to form a string of 8 letters we can make use of any of the available 26 letters.

so the first letter can be selected from 26 in 26 ways,

similarly 2nd letter can be chose in 26 ways..

All the 8 letters as 26*26*26..26 (8 times)= (26)^8

b. simlar procedure but the numbers are not to be repeated,

first letter can be choosen in 26 ways,

2nd letter ->25 ways as on of the 26 has been choosen for the first letter,

3rd letter->24

.

.

this results in 26*25*24*23*22*21*20*19

c. as there is a compulsion on the four letters to be choosen as MC and ER in that particular order itself, the remaining four letters can be chose (26)^4

if letters cannot be repested 22*21*20*19

d. 5 letters occupy their positions in the given order,

remaining 3 can be choosen in 21*10*19 ways

e. given set {T,I,O,N}

first letter can be choosen from the four =>4 ways

second=>4 ways (as the letters can be repeated)

similarly the remaining number of letters,

totally=> 4*4*4*4.. (8 times)

=>4^8

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.