>FWIW, one of the tests of how random a random number generator is is how many numbers you have to generate to get all the numbers in a particular sequence. If the sequence has n values, you definitely don't expect n random numbers to get one of each. The test is called the Coupon Collectors Test.
Yup, if you want 75 numbers in random order, you make a list with these 75 numbers, take a random one and remove it from the list... until the list is empty.