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20 Oct 2016, 21:02
Kudos
Bookmarks
There 4 Apples in a Basket ,5 Mangoes in another basket ,2 Kiwis in another basket in a fruit shop
consider each fruits in the basket are of same colour, shape , size and weight another way to say fruits of its kind in the baskets are identical
1)In how many ways I can select at least one fruit
5*6*3 = (90-1) 89 ways[ where 1 is non selection ]
2)In how many ways I can select so that one fruit is selected from each fruit basket
4*5*6 = 90 ways
Above all are bookish way to get answer, I failing to understand how did they came into these numbers
As per the rule for selecting identical items :-
There only one way to select identical for any number of selection
As per the above statement when there are 4 apples of same kind in a basket
The ways of selecting apples are
Case 1:-
Selecting 4 apples
Selecting 4 apples is one way
and not selecting 4 apples is another way, hence it is 2 ways.
Case 2 :-
Similarly selecting 3 apples
Selecting 3 apples is one way
and not selecting 3 apples is another way, hence it is 2 ways.
Similarly selecting 2 apples
Selecting 2 apples is one way
and not selecting 2 apples is another way, hence it is 2 ways.
Similarly selecting 1 apples
Selecting 1 apples is one way
and not 1 apple selecting is one way, hence it is 2 ways.
Hence the total ways is 2 to the Power 4 and it is 16 ways
which is same as of selecting 4 different numbered\Weighted Apple or distinct type of apples in the basket
Getting confused here, can somebody help?
consider each fruits in the basket are of same colour, shape , size and weight another way to say fruits of its kind in the baskets are identical
1)In how many ways I can select at least one fruit
5*6*3 = (90-1) 89 ways[ where 1 is non selection ]
2)In how many ways I can select so that one fruit is selected from each fruit basket
4*5*6 = 90 ways
Above all are bookish way to get answer, I failing to understand how did they came into these numbers
As per the rule for selecting identical items :-
There only one way to select identical for any number of selection
As per the above statement when there are 4 apples of same kind in a basket
The ways of selecting apples are
Case 1:-
Selecting 4 apples
Selecting 4 apples is one way
and not selecting 4 apples is another way, hence it is 2 ways.
Case 2 :-
Similarly selecting 3 apples
Selecting 3 apples is one way
and not selecting 3 apples is another way, hence it is 2 ways.
Similarly selecting 2 apples
Selecting 2 apples is one way
and not selecting 2 apples is another way, hence it is 2 ways.
Similarly selecting 1 apples
Selecting 1 apples is one way
and not 1 apple selecting is one way, hence it is 2 ways.
Hence the total ways is 2 to the Power 4 and it is 16 ways
which is same as of selecting 4 different numbered\Weighted Apple or distinct type of apples in the basket
Getting confused here, can somebody help?
Archived Topic
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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
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22 Oct 2016, 10:52
Kudos
Bookmarks
joepc
Here's the first part of your error. If there are four apples in the basket, then 'selecting two apples' and 'not selecting two apples' are the same thing. (In both cases, you'll end up with two apples in your hand and two left over in the basket). Likewise, 'selecting three apples' and 'not selecting one apple' are the same thing. (You'll end up with three apples in your hand and one left in the basket.)
Quote:
Here's the second problem. You don't multiply the cases together, you just count them! If you multiply them together, what you'd be counting is the number of ways of picking two apples, AND not picking two apples, AND picking one apple, AND not picking one apple, AND picking three apples, etc. That is, multiplication goes with 'and'.
Instead, you just count up the cases.
Case 1: You pick 4 apples.
Case 2: You pick 3 apples.
Case 3: You pick 2 apples.
Case 4: You pick 1 apple.
Case 5: You pick no apples.
That's five cases in total.
To continue the analogy, you add, or count cases, when you have an 'or' in the problem. You want to pick either two apples, OR three apples, OR one apple, OR no apples, etc. So, you add rather than multiplying.
There are 5 cases for apples, 6 for mangoes, and 3 for kiwis.
You multiply those numbers together, because you're back with 'and' again. You're picking apples AND mangoes AND kiwis. So, 5*6*3 = 90.
But can you work out why we subtract 1 at the end?
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
