a. How many integers are there from 10 through 99?
b. How many odd integers are there from 10 through 99?
c. How many integers from 10 through 99 have distinct digits?
d. How many odd integers from 10 through 99 have distinct digits?
e. What is the probability that a randomly chosen two-digit integer has distinct digits? has dis-
tinct digits and is odd?

(a)

The number of integers from 10 throgh 99.

Given information:

Number is 10 to 99.

Concept used:

m and n are integers and m≤n, then the number of integers from m to n inclusive are m−n+1.

Calculation:

The number of integers from 10 to 99 is 99−10+1=90

(b)

The number of odd integers are there from 10 through 99.

(c)

The number of integers from 10 through 99 have distinct digits.

(d)

The number of odd integers from 10 through 99 have distinct digits.

(e)

To find the probability that a randomly chosen two digit integer has distinct digits, then to find the probability that chosen integer has distinct digits and is odd.