The answer depends on what mathematical operations are permitted and on whether or not all four number must be used.
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24C7 = 24!/((24-7)!7!) = 346,104.
There are 24C12 = 24!/[12!*12!] = 2,704,156 combinations.
There are many combinations of 5 numbers which would equal 100, for example...50 + 25 + 20 + 3 + 2 = 10050 + 24 + 19 + 4 + 3 = 10096 + 1 + 1 + 1 + 1 =10017 + 33 + 18 + 31 + 1 = 100 and many, many more.
Three numbers that equal 72 are 24, 24, and 24. Another set of three numbers that equal 72 are 36, 18, and 18. Additionally, 8, 24, and 40 are another set of three numbers that equal 72.
There is an infinite amount of numbers that can sum up to 24. Only 23, if you are just counting positive numbers.