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805+ Level|   Combinations|      
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Bunuel
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The GMAT Math Pro logo is stuck on the highest ledge of a nine-story 27 Nov 2019, 02:14
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25% (02:32) correct 75% (02:42) wrong based on 153 sessions

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The GMAT Math Pro logo is stuck on the highest ledge of a nine-story building and must climb down to the single ledge on the bottom row to get to safety. Each move he makes must be to a ledge on the level immediately below him and to the immediate right or left of the ledge on which he’s currently standing. If all available ledges are pictured in the above diagram, how many paths can he take to get to safety?

A. 18
B. 70
C. 128
D. 256
E. 512


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nick1816
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The GMAT Math Pro logo is stuck on the highest ledge of a nine-story 27 Nov 2019, 05:18
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Total number of ways
= 8C4=70





Bunuel

The GMAT Math Pro logo is stuck on the highest ledge of a nine-story building and must climb down to the single ledge on the bottom row to get to safety. Each move he makes must be to a ledge on the level immediately below him and to the immediate right or left of the ledge on which he’s currently standing. If all available ledges are pictured in the above diagram, how many paths can he take to get to safety?

A. 18
B. 70
C. 128
D. 256
E. 512


Are You Up For the Challenge: 700 Level Questions


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The GMAT Math Pro logo is stuck on the highest ledge of a nine-story 14 Jan 2020, 06:22
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longest route to be taken

LLLLRRRR

8!/(4!*4!)
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The GMAT Math Pro logo is stuck on the highest ledge of a nine-story 02 Mar 2020, 07:58
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nick1816
Total number of ways
= 8C4=70





Bunuel

The GMAT Math Pro logo is stuck on the highest ledge of a nine-story building and must climb down to the single ledge on the bottom row to get to safety. Each move he makes must be to a ledge on the level immediately below him and to the immediate right or left of the ledge on which he’s currently standing. If all available ledges are pictured in the above diagram, how many paths can he take to get to safety?

A. 18
B. 70
C. 128
D. 256
E. 512


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GMATLogoLedges.jpg
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Can you explain further? Thanks a ton!
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The GMAT Math Pro logo is stuck on the highest ledge of a nine-story 04 Aug 2020, 03:49
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metalhead2593
nick1816
Total number of ways
= 8C4=70





Bunuel

The GMAT Math Pro logo is stuck on the highest ledge of a nine-story building and must climb down to the single ledge on the bottom row to get to safety. Each move he makes must be to a ledge on the level immediately below him and to the immediate right or left of the ledge on which he’s currently standing. If all available ledges are pictured in the above diagram, how many paths can he take to get to safety?

A. 18
B. 70
C. 128
D. 256
E. 512


Show Spoiler
Attachment:
GMATLogoLedges.jpg


Can you explain further? Thanks a ton!
Show more

If you observe the image in the problem, there are a total of 8 steps that the person must take to reach the bottom-most ledge. At each stage of this 8 step journey, the person can take only 2 decisions, whether to go right or to go left. However, since the left and right sides are constrained, i.e. a person can take a maximum of 4 left side jumps and 4 right side jumps, we must arrange these 4 lefts and 4 rights in a total of 8 steps.
Mathematically, 8!/(4!x 4!) (division by 4! twice to account for 4 lefts and 4 rights, similar to how we use this approach in problems on arranging words in a series)
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The GMAT Math Pro logo is stuck on the highest ledge of a nine-story 04 Aug 2020, 10:03
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I will try to give a good explanation here

So I will use the combinatorics method to demonstrate nick1816 method

To give you a clue on how we can count , I will assign L and R , meaning that Left and Right , if the guy chooses to go left , I will right L , if right i will write R

One path to reach the bottom is L(to 8th floor) , L(7th) , L(...) , L , R ,R ,R , R(bottom) (use the picture start from the top and then choose left for the first , second , third and fourth step , then you'll have only the right to go to the right bottom ( messing with your head a little).

so I will give you here a hint , all the paths to the bottom need to use 4 Left and 4 right (LRLLLRRR , LRLRLRLR....)
so this problem is a permutation one (Ah ha !!!!!!!!!!!)

since I have 8 choices and 4 repetitions in two sets .

number of roots = 8!/(4! * 4!)= 8C4 =70 Voila !!!!!!!!!!

E is the answer

(permutation rule , to arrange N letters for example , and you have A , B ,C letters repeted X, Y , Z times , then the number of words you can create from this list is N! / (X! * Y! * Z!)

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The GMAT Math Pro logo is stuck on the highest ledge of a nine-story 30 Jun 2022, 18:59
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This is going to be difficult to describe, but I’ll try my best.

If we count each “slot” as 1 unit, what we essentially have is a rhombus with 4 “slot-units” making up each side.

Shift the entire picture counterclockwise so that the stick man at the top is now in the bottom left corner.

The picture is then the “standard” picture in which the person can only travel East or North until he travels from the bottom-left corner to the upper-right corner of the figure.
However, instead of a perpendicular square, we have a bit of a “stretched” rhombus. The same logic still applies.

No matter which path you take, you will always be making 4 “Eastward” moves and 4 “Northward” moves.

E-E-E-E-N-N-N-N

Then just find the number of ways to arrange the 8 elements, of which 4 “E’s” are identical and 4 “N’s” are identical.

8! / (4! * 4!) = 70 ways

Clever way to alter the common question so as to make it more daunting. Great question!

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The GMAT Math Pro logo is stuck on the highest ledge of a nine-story 01 Jul 2022, 02:40
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Whatever path one takes, to reach the single bottom ledge, one has to take 4 left ledges and 4 right ledges.

One of the ways will be LLLLRRRR.

The total number of paths will be all the arrangements of the above path.

Thus, the total number of paths = 8!/4!*4! = 8*7*6*5/4*3*2*1 = 70 ways.

Thus, the correct option is B.
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The GMAT Math Pro logo is stuck on the highest ledge of a nine-story 02 Jan 2025, 22:08
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