You have a chance to win a prize by picking 5 numbers from 42, (no repeat) what is your chance to win if:

a. order is important

b. order is not important

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- Mar 1st 2009, 01:46 PM #1

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- Feb 2009
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- Mar 1st 2009, 03:03 PM #2
Assuming the numbers are not replaced after each draw:

a. $\displaystyle (\frac{5}{42}) (\frac{4}{41}) (\frac{3}{40}) (\frac{2}{39}) (\frac{1}{38}) = \frac{5!}{(42)(41)(40)(39)(38)}$

b. $\displaystyle ^nC_r = \frac{n!}{(n-r)!r!} $ where n = 42 and r = 5

= $\displaystyle \frac{42!}{(42-5)!5!}$