Question: 1. In how many ways can 1 professor and 5 students can be taken from 4 professors and 10 students.
2.Given -1 Answer: 1. The number of ways of choosing 1 professor and 5 students is
(number of ways of taking 1 professor from among 4) * (number of ways of taking 5 students from 10)
This is
(4) * (10*9*8*7*6 / 5!), where the 5! in the second term accounts for rearranging 5 of the students, i.e. 5! is the number of ways of reordering the group of any particular 5 students.
In formulas,
4!/(1! 3!) * 10!/((10-5)! 5!)
2. Can you order these numbers? For example, x^2 is smaller than x in MAGNITUDE, but is POSITIVE, so I think the correct order is
-1, x, x^3, x^2, 1,
where 0 would come between x^3 and x^2. This means the median is x^3.
3. Let's think about this. For a number to have its square root less than 2000, it has to be less than 4,000,000 or so. For a number to have its CUBE root less than 2,000, it should be less than 8,000,000,000. You can come up with these numbers by squaring and cubing 2000, respectively.
This would indicate that the square root is the stricter criteria, and that there are 4,000,000 numbers with square root and cube root between 1 and 2000, if those numbers are included.
You didn't happen to mention whether the cube root and square root have to be integers. For example, if we take the square root of 1,236,544, we get 1,112, but the cube root of that is 107.333. Does that count? If not, I think I can come up with an approach to count all the number with square root and cube root that are INTEGERS between 1 and 2000, e.g. 9,261, but that might be more compllicated.Related Questions
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