Can you help me to find out the solution of this problem and explain the answer?
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What do you call a "variety" ? Do you mean plainly that there a 21 donuts ? But in this case, the result is not understandable. – Jean Marie Nov 02 '16 at 10:26
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@JeanMarie I mean different tests. – Hazem Alabiad Nov 02 '16 at 10:27
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Sorry, but, in this case, what do you call a "test" ? I am pretty certain that something is missing in your question. – Jean Marie Nov 02 '16 at 10:29
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@JeanMarie I think he means taste – H. Potter Nov 02 '16 at 10:30
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@JeanMarie It was an exam question ... the Q is correct .. – Hazem Alabiad Nov 02 '16 at 10:35
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@JeanMarie I got it ... Thanks guys ... – Hazem Alabiad Nov 02 '16 at 11:21
1 Answers
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$\binom{21+6-1}{6} = $230230 Or $\binom{21+6-1}{20} = $230230
Using starts and bars method: For 21 varieties we need 20 bars for selecting the items. Then, we will have (20+6) or (21+6-1) choices '6' stars or (donuts) and '20' to separate the different kinds of donuts (as in the Q: Varieties) as shown below:
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Or: |**|*|** ..... *|*
And from these options we can either select the 6 donuts "Starts"
or, the 20 "Bars" which we use to separate between tests.
Hazem Alabiad
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*stars and bars, but thats only a typo i guess (even tho you use starts twice, so...). Much better then before, but i hope you yourself understand it too. – SAJW Nov 03 '16 at 09:21