## Friday, February 11, 2011

### Biggest Loser

In the most recent Biggest Loser competition, the contestants had to arrange the order of five dishes from least calories to most.  If they did it blind-folded, how many different ways could the food be arranged?

But let's say they have some knowledge about a couple of the dishes.  They know the plate of hamburger (loaded with everything) and chips should be near the top, while the plate of broccoli should be near the bottom of the scale.  How does that affect the number of choices?

#### 1 comment:

1. Without any knowledge of the dishes: 5*4*3*2*1=120
After knowing the plate of hamburger and chips should be ranked second and the plate of broccoli be ranked fourth(Is that what you meant by "near the top/bottom"? I'm not a native speaker:)): 3*(1*)2*(1*)1=6
So the number of choices in the second case will be 20 times smaller than that in the first case.

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