SOLUTION: how many samples of size 3 can be drawn from s={2,4,8,10,12,}, (a) with replacement, (b) without replacement

Question 251685: how many samples of size 3 can be drawn from s={2,4,8,10,12,}, (a) with replacement, (b) without replacement
Found 2 solutions by stanbon, jrfrunner:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
how many samples of size 3 can be drawn from s={2,4,8,10,12,},

(a) with replacement: 5^3 = 125
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(b) without replacement: 5P3 = 5*4*3 = 60
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Cheers,
Stan H.

Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website!
there are 4 scenarios
1. Order is important and with replacement
in this case each of the three times there are five choices: 5*5*5 =5^3=125
2. order is important and without replacement
in this case you decrement the choices as each is selected: 5*4*3= 60
3. Order is NOT important and with replacement
in this case choice 2,4,8 is the same as 8,4,2 or 4,2,8 etc
so the number of ways is (n+k-1)C(k) where n=number of choices, k=selected
or (5+3-1)C3 = 7C3 = 35
4. order is NOT important and without replacement
in this case the number of ways is 5C3=10
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