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16 Sep 2014, 05:38
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Hello, I am So confused as I thought all combinatorics can be estimate using formulas. However I couldn't figure out how to work out the following and it makes me a bit nervous. Please could anyone show me how to do it if we cannot draw all combinations during GMAT?
Your help will be much appreciated! And I like to give KUDOS!
Resources: GMAT Club Math book
Gordon
Example #1
Q:. There are three marbles: 1 blue, 1 gray and 1 green. In how many ways is it possible to arrange marbles in a row?
Solution: Let's write out all possible ways:
Answer is 6.
gordonf35: This answer is abvious, which is 3!
In general, the number of ways to arrange n different objects in a row
Example #2
Q:. There are three marbles: 1 blue, 1 gray and 1 green. In how many ways is it possible to arrange marbles in a row if blue and green marbles have to be next to each other?
Solution: Let's write out all possible ways to arrange marbles in a row and then find only arrangements that satisfy question's condition:
Answer is 4.
Example #3
Q:. There are three marbles: 1 blue, 1 gray and 1 green. In how many ways is it possible to arrange marbles in a row if gray marble have to be left to blue marble?
Solution: Let's write out all possible ways to arrange marbles in a row and then find only arrangements that satisfy question's condition:
Answer is 3.
Your help will be much appreciated! And I like to give KUDOS!
Resources: GMAT Club Math book
Gordon
Example #1
Q:. There are three marbles: 1 blue, 1 gray and 1 green. In how many ways is it possible to arrange marbles in a row?
Solution: Let's write out all possible ways:
Answer is 6.
gordonf35: This answer is abvious, which is 3!
In general, the number of ways to arrange n different objects in a row
Example #2
Q:. There are three marbles: 1 blue, 1 gray and 1 green. In how many ways is it possible to arrange marbles in a row if blue and green marbles have to be next to each other?
Solution: Let's write out all possible ways to arrange marbles in a row and then find only arrangements that satisfy question's condition:
Answer is 4.
Example #3
Q:. There are three marbles: 1 blue, 1 gray and 1 green. In how many ways is it possible to arrange marbles in a row if gray marble have to be left to blue marble?
Solution: Let's write out all possible ways to arrange marbles in a row and then find only arrangements that satisfy question's condition:
Answer is 3.
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16 Sep 2014, 22:41
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gordonf35
Example 2:
If two things are to be next to each other, imagine that you bind them with a string and they become one. Now you effectively have to arrange 2 things which can be done in 2! ways. But the marbles tied together can be tied in two ways Blue-Green or Green-Blue. Hence we need to multiply 2! by another 2 to get 4 total ways of arranging.
Example 3:
Total number of ways of arranging 3 marbles is 3! = 6. In half of these, Blue marble will be to the left of Gray marble and in the other half, Blue marble will be to the right of Gray marble. Hence number of ways such that Blue marble is to the left of Gray marble is 6/2 = 3 ways.
Also, check out the posts below. They discuss these concepts in detail and remember, formulas will only take you to 500-550 in GMAT. Thereafter, you will need logic.
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/10 ... inatorics/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/10 ... ts-part-i/
(Ignore the first question discussed in this post)
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/10 ... s-part-ii/
18 Sep 2014, 09:47
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VeritasPrepKarishma
Thanks for your reply. However, i thought question 3 said "gray marble have to be left to blue marble", so we should actually treat these 2 as 1 element. So 3! / 2!, which is 3. Am i correct?
