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Counting Number of Possible Hand Gestures 
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#1
Oct2711, 01:55 PM

P: 7

Hi All,
I'm terribly stuck on this problem. We were asked to calculate how many hand gestures are possible, keeping in mind that a hand gesture consists of raising one or both hands and extending some fingers (note: raising just a fist is also considered a gesture). I started this problem by thinking of doing 3*5 (representing 1 finger raised on right, left or both hands) * 3*((510)) but something seems off. My professor suggested looking at Pascal's Triangle, but I'm not sure where to go from there. Any suggested would be so helpful! Thanks! 


#2
Oct2811, 11:18 AM

Sci Advisor
P: 906

let's just look at the possible gestures involving a single hand.
each gesture might involve 0  5 fingers. for 0 fingers, there is one possible gesture ("the fist"). for 1 finger, there are 5 possible gestures (assuming we count the "thumb" as a finger) in general, for k fingers there are 5 choose k (i will write this as 5Ck). the general formula for this is 5!/(k!(5k)!). for 5C3, this is 120/(6*2) = 10, for example. so we have: 5C0 + 5C1 + 5C2 + 5C3 + 5C4 + 5C5 gestures that is, 1 + 5 + 10 + 10 + 5 + 1 = 32 (this is the sum of the 5th row of pascal's triangle). i think you can take it from here.... 


#3
Oct2811, 11:28 AM

P: 12

I like to think i'm capable of expressing myself using my hands in an infinite number of ways.



#4
Oct3011, 11:35 PM

P: 1

Counting Number of Possible Hand Gestures
How many gestures with the restriction that you cannot extend a ring finger unless you also extend the middle finger next to it?
How many gestures with the restriction that you may not extend the middle finger alone on either hand? I can get the numbers for 0,1,2,8,9,10 fingers for each by writing out combinations but I can't come up with a simpler mathematical solution for anything in the middle. It just seems like there's too many cases to consider for each. But perhaps I'm overthinking it. 


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