WeBWorK at McNeese Sta webwork / u18-math 130b-hardee /4.1 homework / 2 4.1 Home

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WeBWorK at McNeese Sta webwork / u18-math 130b-hardee /4.1 homework / 2 4.1 Homework: Problem 2 Previous Problem ListNext (1 point) How many strings of five uppercase English letters are there (a) that start and end with the letters B0 (in that order), if letters can be repeated? (b) if no letter can be repeated? c)that start or end with the eters BO (m the or en riet ers can berepealer?nous eon (d) that start and end with an X, if letters can be repeated? Note: You can earm partial credit on his problenm Preview My Answers Submit Answers You have attempted this problem O tmes You have unlimited attempts remaining nstructor Page geteated at06/122018 ? 01 39pm CDT

Explanation / Answer

(a) Out of the five letters of the strings, four letters are already fixed with two letters BO at the start and the same two letters BO at the end.

Thus, only the middle letter is left which can be any of the 26 letters.

Thus, number of required strings = 26

(b) If no letter can be repeated, no of strings = 26*25*24*23*22= 7893600

(c)Case 1:

No. of ways in which the string start with the letters BO = 26*26*26

Case 2:

No. of ways in which the string end with the letters BO = 26*26*26

Case 3:

When the string start and both with letters BO

No. of ways = 26.

Thus, required no. of ways = 35178

(d) If the string start and end with X, the middle 3 letters can have 26*26*26 arrangements.

Thus, no. of ways = 17576

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