1. Suppose in a university, each subject offered to students has a subject code consisting ofthree letters followed by five digits.i.How many different subject codes are possible? [3M]ii.How many subject codes could begin with CS and end with digit 3 or 2? [4M]iii.How many subject codes are possible in which all the letters and the digits aredistinct? [3M]

Answered: Image /qna-images/answer/eb07e949-3994-4f89-be57-cc16c9b744fe.jpg

Answered: 1. Suppose in a university, each…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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How many different 6-letter words can be made a. if the first letter must be E or W and no letter may be repeated? b. if repeats are allowed (but the first letter is E or W)? c. How many of the 6-letter words (starting with E or W) with no repeats end in H?
A class has 32 students. In how many different ways can six students form a group for an activity? (Assume the order of the students is not important.) There are different ways that the six students can form a group for an activity. (Type a whole number.)
2.Find the number of 6-letter words that use letters from {A,B,C,D,E} in which no 5 consecutive letters are all the same. (Hint. First count the words that you don'twant to include.)
Japanese license plates in each state consist of 8 characters. The first two characters can be any digit (0 to 9) and may be repeated. The third character can be one of 32 different hiragana letters, and the fourth is one of the 5 vehicle types. The last four characters, are digits (0 to 9), but may not be repeated. How many different license plates are possible?
How many three – digit numbers can be formed fromthe digits 1, 2, 5, 6, and 9 if each digit can be usedonly once? 6.1 From the answer above, in how many area. even? b. Odd? c. Numbers greater than 600? d. How many three digit numbers can be formedif repetition is allowed?
3. Your student email account requires you to choose a password of 4 letters followed by 1 of the digits 0 -9. The password can consist of upper case letters (26) or lower case letters (26). How many different five-character passwords can be created? 4. At a swim meet, 8 different swimmers compete in the 800 meter freestyle race. How manydifferent ways are there for these swimmers to finish?
Jessie is creating a 10-character password that consists ofnumbers and letters (Each digit will be considered a character). He isnot allowed to have repeated characters, but lower case letters andupper-case letters are allowed (ex. “a” and “A” will be considereddifferent characters).a. How many different passwords can he create if “a” and “A” mustbe a part of the password. b. How many different passwords can he create if there must beat least 8 digits in the password?
3. How many three digit numbers can be formed from the set 0, 1, 2, 3 ......... if repetitions are not allowed and the number must be divisible by a. 10 ? b... 25? c. even?

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