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# probability or combination

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Manager
Joined: 05 Oct 2005
Posts: 200
Followers: 1

Kudos [?]: 1 [0], given: 0

probability or combination [#permalink]  24 May 2006, 00:07
hello
plz need help on the following
when dealing with question like this one

The only contents of a bag are 4 pens that write blue and 3 pens that write green. If 4 of those pens are chosen at random, what is the probability that 2 of the pens write blue and 2 of the pens write green?

A) 2/7

B) 1/2

C) 18/35

D) 4/7

E) 9/14
I don 't know when to use simple probability or combination
usually permutations and combination deal with the number of ways

i am quite lost

thanks
_________________

when there is a will there is a way

best regards

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Senior Manager
Joined: 09 Mar 2006
Posts: 445
Followers: 1

Kudos [?]: 6 [0], given: 0

Probability of certain outcome is always equal to the number of
successful outcomes divided by the number of total possible outcomes.

Total outcomes = 7C4
Successful = 4C2 (for blue pens ) * 3C2 ( for green ones )

4C2*3C2 / 7C4 = 18/35
SVP
Joined: 30 Mar 2006
Posts: 1737
Followers: 1

Kudos [?]: 46 [0], given: 0

Method One: Using Simple probability

4 pens in which 2 will write blue and 2 will write green. Hence possible combinations

BBGG
BGBG
GBGB
GGBB
GBBG
BGGB

Each has a probability of 3/35 (from 4/7*3/6*3/5*2/4)

Hence total probability = 6*3/35 = 18/35

Method 2:

THere are 7C4 ways 4 pens can be chosen.
two blue can be chosen 4C2 ways and 2 green can be chosen in 3C2 ways

Therefore, P = (4C2*3C2)/7C4 = 18/35
Manager
Joined: 09 May 2006
Posts: 99
Location: Bangalore, India
Followers: 2

Kudos [?]: 13 [0], given: 0

Agree with 18/35.

Even I had problems with these type of questions as one gets confused whether to treat it as 'with replacement' or without.

I think the approach is to treat each similar coloured object (pens, marbles etc) as unique - calculate number of combinations for one colour - then mutiply with number of combinations for other colour to get total number of ways for the condition to be true.

To get probability we devide with total number of ways possible, which is given by nCr.
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