Answer
a. 9000 integers
b. 4500 odd integers
c. 4536 integers with distinct digits
d. 2240 odd integers with distinct digits
e. 50.4% probability for a random 4-digit integer with distinct digits
24.9% for random 4-digit odd integer with distinct digits
Work Step by Step
a. 9*10*10*10 = (9999 – 1000) + 1 = 9000 integers
b. 9*10*10*5 = ((9999 – 1000) + 1)/2 = 4500 odd integers
c. 9*9*8*7 = 4536 integers with distinct digits
d. 5*8*8*7 = 2240 odd integers with distinct digits
5 (4th digit is odd) *
8 (1st digit not zero and not matching the last digit) *
8 (2nd digit not matching last and 1st and 4th digits) *
7 (3rd digit not matching 1st, 2nd, 4th digits) = 5*8*8*7 = 2240
e. 4536/9000 = 504/1000 = 63/125 = 50.4% probability for a random 4-digit integer with distinct digits
2240/9000 = 224/900 = 56/225 = 24.9% for random 4-digit odd integer with distinct digits