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arjtryarjtry
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In a certain game, a one-inch square piece is placed in the 02 Aug 2008, 02:24
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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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durgesh79
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In a certain game, a one-inch square piece is placed in the 02 Aug 2008, 12:18
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arjtryarjtry
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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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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In a certain game, a one-inch square piece is placed in the 05 Aug 2008, 02:09
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arjtryarjtry : OA pls
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In a certain game, a one-inch square piece is placed in the 05 Aug 2008, 04:53
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arjtryarjtry
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
Show more

This will happen when number of up moves = Number of right moves = 4
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bhushangiri
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In a certain game, a one-inch square piece is placed in the 05 Aug 2008, 05:26
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durgesh79
arjtryarjtry : OA pls
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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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In a certain game, a one-inch square piece is placed in the 05 Aug 2008, 06:29
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there is another way to calculate total number of chances ...
expand binomial expression (1+1)^8 = 2^8 = 256



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