Question 237633: 100C2 has a value of 4,950, what is the value of 100C98?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 100C2 has a value of 4,950, what is the value of 100C98?
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It is the same number.
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Why?
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100C2 is a count of the number of sets of two you can draw
from a set of 100 items.
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But every time you draw a set of 2 from 100 you have
automatically determined a set of 98 that you did
not select.
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The number of sets you did not select = the number
of sets you collected. So the count is the same.
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In general nCk = nC(n-k)
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Try it: 8C2 = (8*7)/(1*2) = 28
8C6 = (8*7*6*5*4*3)/(1*2*3*4*5*6) = (8*7)/(1*2) = 28
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Cheers,
Stan H.
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