Question

In Discrete Math,

1. a. There are 689 students, 112 of them have earned at least 60 credit hours and 78 of them have earned at most 60 credit hours. How many students are there who have accumulated exactly 60 hours?

b. Find the total number of positive integers between 0 and 99 that end with 3.

c. A standard Pennsylvania State license plate consists of three letters followed by four digits. Determine the number of standard Pennsylvania State license plates with B as the first letter or 5 as the first digit.

Answer 1

1)

number of student who have accumulated exactly 60 hours = 112 -78 = 34

2)

total number of positive integer = way of selecting any digit from 0 to 9 * way of selecting last digit is 3

= 10 *1 = 10

3)

number of plate having first letter is B= way of first letter is B * remaining 2 letter is any 26 letter * next 4 digit is number

=1*26 C 2 * 10C4

= 1*26*25/2* 10*9*8*7/24= 68250

number of plate having first number is 5 = 26C3 * 1*10C3

=26*25*24/6*10*9*8/6= 312000

having both conditions = 1*26C2*1*10C3= 26*25/2*10*9*8/6= 39000

total number of plate =   68250 +312000 - 39000= 341250