In a lottery 5 different numbers are chosen from the first 90positive integers.
(a) How many possible outcomes are there? (An outcome is anunordered sample of five numbers.)
(b) How many outcomes are there with the number 1 appearingamong the five chosen numbers?
(c) How many outcomes are there with two numbers below 50 andthree numbers above 60?
(d) How many outcomes are there with the property that the lastdigits of all five numbers are different? (The last digit of 5 is 5and the last digit of 34 is 4.)
