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A college teaches 7 different courses. Students from the college are to be randomly selected for a college survey. How
many students must be selected to ensure there are at least 5 students from one of the courses?
A club athletics team consisting of 1 male and 1 female long distance runner and 2 male and 2 female sprinters is to be
selected from 5 male and 7 female long distance runners and 3 male and 5 female sprinters. The team captain is to be one
of the female sprinters. In how many different ways can the team be created?
In how many ways can a car yard display of 10 cars be created if it must consist of a combination of Mercedes, BMWs,
Fords and Subarus and the display must contain at least 1 car from each manufacturer?
1. i)12+ 22+ 32 +..4n2= {n(n#1)(2n+1)} / 6 — for n ? 1
Proof for n =1, the statement reduces to 1? = 1.2.3/ 6 and is obviously true.
Assuming that the statement is true for n=k
12422 + 32 +.4 k2 = {k (k+1) (2k+1)} /6...........................(i)
We will prove that the statement must be true for n= k#1
12422 + 32 4.4 (k + 1)2= {(k +1) (k #2) (2k+3)}...........................(ii) Read More
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