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?
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
ELEMENTARY ,DEAR WATSON
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