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TexMex Take-out (Posted on 2007-02-25) Difficulty: 3 of 5
A restaurant offers a take-out deal where any combination of 10 items can be purchased for $5. The menu choices are divided into five types: Tacos, Burritos, Tamales, Chiles Rellenos, and Chimichangas. For example, a person could order 2 Tacos, 4 Burritos, a Tamal and 3 Chimichangas. Or maybe 7 Tamales and 3 Chiles Rellenos. Or perhaps 10 Chimichangas and nothing else. How many different ten-item combinations are available?

No Solution Yet Submitted by hoodat    
Rating: 4.5000 (2 votes)

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Solution sheherezade | Comment 1 of 2

Answer: 1001

Explanation: a model of selecting ten  items of  5 types is

evaluating  the total   QUANTITY of     14 digit numbers consisting of 4 onEs and 10 zeroes;

:  e.g  00001001100001 means:

4 tacos,2 burritos, no tamales,4 chlIes and no cimimichangas

So  we have to select where to place the 4 ones- partition signs

c(14,4)=   14*13*12*11/ 1*2*3*4= 7*13*11=1001


  Posted by Ady TZIDON on 2007-02-25 16:10:33
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