Consider all the three digit positive integers Note a three

Consider all the three digit positive integers. (Note: a three digit integer does not contain leading zeros.) a) How many are odd and do not contain the digit 5? b) What is the probability that a 3 digit positive integer is odd and does not contain the digit 5? c) What is the probability that a 3 digit positive integer has all the digits the same? d) What is the probability that a 3 digit positive integer has all the digits different?

Solution

a)

Unit digit -1,3,7,9
Tenth digit -0,1,2,3,4,6,7,8,9
100th digit -0,1,2,3,4,6,7,8,9


The total possible ways =4*9*9=324
Since in the unit digit there are 4 integers, there exist 9*4=36 redundant 3 digits integer.

therefore 324-36=288 different 3 digit integer is the answer.

b)

100-999 3 -digit integers, 900/2=450 odd numbers.

Units digit should contain {1,3,7,9} = 4; Tens digits can be {0,1,2,3,4,6,7,8,9} = 9 Hundreds digit can be {1,2,3,4,6,7,8,9} = 8.

So the answer is 894 = 288

Probability is 288 / 450 = 0.64

c and d)

please post it in a new question