Expert: Sherman D. - 5/26/2006

Question
how many different sets of six numbers each are possible to make from integers 1 to 45

Answer
If you are saying 1,2,3,4,5,6 and 2,3,4,5,6 as being 2 different sets then
46C6 = 9366819 possible sets

nCr = (n!)/(r!(n - r)!)
10C6 = (46!)/(6!(46 - 6)!)
10C6 = (46!)/(6! * 40!)
10C6 = (46*45*44*43*42*41)/(6*5*4*3*2*1)
10C6 = (45/5) * (42/6) * (44/4) * (46/2) * (41/1) * (43/3)
10C6 = 9 * 7 * 11 * 23 * 41 * (43/3)
10C6 = (9 * (43/3)) * 7 * 11 * 23 * 41
10C6 = (3 * 43) * 7 * 11 * 23 * 41
10C6 = 3 * 43 * 7 * 11 * 23 * 41
ANS : 9366819

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But if you mean 1,2,3,4,5,6 and 6,4,3,1,2,5 as being 2 different sets
46P6 = 6744109680 possible sets

Mathematically Done
nPr = (n!)/((n - r)!)
10P6 = (46!)/((46 - 6)!)
10P6 = (46!)/(40!)
10P6 = 46 * 45 * 44 * 43 * 42 * 41
ANS : 6744109680

Info found at http://mathforum.org/dr.math/faq/faq.comb.perm.html