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In a certain game, a one-inch square piece is placed in the

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In a certain game, a one-inch square piece is placed in the [#permalink] New post 02 Aug 2008, 01:24
In a certain game, a one-inch square piece is placed in the lower left corner of an eight-by-eight grid made up of one-inch squares. If the piece can move one grid up or to the right, what is the probability that the center of the piece will be exactly 4sqrt(2) inches away from where it started after 8 moves?

24/256

64/256

70/256

128/256

176/256

PLS GIVE EXPLANATION IF POSSIBLE WITH DIAGRAM....
IT WOULD BE VERY HELPFUL
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Re: SQUARES PROBABILITY [#permalink] New post 02 Aug 2008, 11:18
arjtryarjtry wrote:
In a certain game, a one-inch square piece is placed in the lower left corner of an eight-by-eight grid made up of one-inch squares. If the piece can move one grid up or to the right, what is the probability that the center of the piece will be exactly 4sqrt(2) inches away from where it started after 8 moves?

24/256

64/256

70/256

128/256

176/256

PLS GIVE EXPLANATION IF POSSIBLE WITH DIAGRAM....
IT WOULD BE VERY HELPFUL


imagine xy plane with intial position of piece at (0,0)
it can move 8 places in right or up direction

distance will be 4sqrt(2) when the final location is (4,4)

Final location - number of ways to reach there
(0,8) ---------- 8C0 = 1
(1,7) -----------8C1 = 8
(2,6)------------8C2 = 28
(3,5)------------8C3 = 56
(4,4)------------8C4 = 70 ....... (frankly i stopped here and marked option C .. but i dont recommend it)
(5,3)----same as (3,5) = 56
(6,2)------- = 28
(7,1)-------- = 8
(8,0)--------- = 1

probablity = 70/sum = 70/256.... answer
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Re: SQUARES PROBABILITY [#permalink] New post 05 Aug 2008, 01:09
arjtryarjtry : OA pls
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Re: SQUARES PROBABILITY [#permalink] New post 05 Aug 2008, 03:53
arjtryarjtry wrote:
In a certain game, a one-inch square piece is placed in the lower left corner of an eight-by-eight grid made up of one-inch squares. If the piece can move one grid up or to the right, what is the probability that the center of the piece will be exactly 4sqrt(2) inches away from where it started after 8 moves?

24/256

64/256

70/256

128/256

176/256

PLS GIVE EXPLANATION IF POSSIBLE WITH DIAGRAM....
IT WOULD BE VERY HELPFUL


This will happen when number of up moves = Number of right moves = 4
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Re: SQUARES PROBABILITY [#permalink] New post 05 Aug 2008, 04:26
durgesh79 wrote:
arjtryarjtry : OA pls


Don D,

I concur with your answer.. used gyan imparted by u in ur recent solution on 3,2 football match.. arrange n items where x are of type 1 and y are of type 2. n!/ x!y! :)

for (0,8) arrange 8 steps where 8 are of 1 type and 0 of another = 8!/8! = 1. (8,0) is also 1. total 2
for (1,7) and (7,1) arrange 8 steps where 7 are of 1 type and 1 of another. 8!/(7! 1!)= 8. 16 total.

similarly for 2,6 and 6,2 8!/(6! 2!) = 28. 56 total

for 3,5 and 5,3 8!/3!5! = 56. total 112

4,4 8!/4!4! = 70.

grand total = 70+112+56+16+2 = 256

favorable case = 70

prob = 70/256
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Re: SQUARES PROBABILITY [#permalink] New post 05 Aug 2008, 05:29
there is another way to calculate total number of chances ...
expand binomial expression (1+1)^8 = 2^8 = 256
Re: SQUARES PROBABILITY   [#permalink] 05 Aug 2008, 05:29
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