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by JeetGulia » Sun Aug 01, 2010 3:07 am
A boy has 6 different pockets and 4 different coins. In how many ways can he put these coins in pockets.

a)1296

b)4096

c) 24

d) 10

e) 240.
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by outreach » Sun Aug 01, 2010 3:33 am
is it 24?

1 coin can go to any of 6 pockets...= 6
2 coin can go to any of 6 pockets...= 6
3 coin can go to any of 6 pockets...= 6
4 coin can go to any of 6 pockets...= 6

24
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by kvcpk » Sun Aug 01, 2010 3:38 am
JeetGulia wrote:A boy has 6 different pockets and 4 different coins. In how many ways can he put these coins in pockets.

a)1296

b)4096

c) 24

d) 10

e) 240.
Only 4 pockets are needed for putting 4 coins.
picking 4 pockets from 6 pockets = 6c4 = 15 ways.
Now, out of these 4,
each pocket can be filled in 4 ways.
total number of ways here = 4*4 = 16.
Hence Total = 16*15 = 240 ways.

Whats the OA?
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by this_time_i_will » Sun Aug 01, 2010 5:02 am
There are 6 diff pockets and 4 diff coins. SInce more than one coin can go to one pocket we will have 6^4 = 1296.
I think A.
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by JeetGulia » Sun Aug 01, 2010 5:56 am
this_time_i_will wrote:There are 6 diff pockets and 4 diff coins. SInce more than one coin can go to one pocket we will have 6^4 = 1296.
I think A.
..Yo...you are the champ!!

1296
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by Brent@GMATPrepNow » Sun Aug 01, 2010 5:59 am
JeetGulia wrote:A boy has 6 different pockets and 4 different coins. In how many ways can he put these coins in pockets.
a)1296
b)4096
c) 24
d) 10
e) 240.
Very nice question. Here's my approach:

For every counting question, I always ask, "Can I take the task and break it into stages?"
Here, the answer is yes.

Stage 1: Place coin #1 in one of the 6 pockets.
Stage 2: Place coin #2 in one of the 6 pockets.
Stage 3: Place coin #3 in one of the 6 pockets.
Stage 4: Place coin #4 in one of the 6 pockets.

Then determine the number of ways to accomplish each stage.

Stage 1: 6 ways (place in pocket 1, 2, 3, 4, 5, or 6)
Stage 2: 6 ways (place in pocket 1, 2, 3, 4, 5, or 6)
Stage 3: 6 ways (place in pocket 1, 2, 3, 4, 5, or 6)
Stage 4: 6 ways (place in pocket 1, 2, 3, 4, 5, or 6)

By the Fundamental Counting Principle, we can find the number of ways to complete the entire task by multiplying the number of ways to accomplish each stage.

So, total = 6x6x6x6 =6^4 ways (aka 1296 ways)

Answer = A
Brent Hanneson - Creator of GMATPrepNow.com
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