A little problem for you. Here's the question: I have three fruits, each of the three fruits have 7 different flavors, I want to mix and match every possible flavor you could generate by mixing and matching how many would I have

You can think this one through like this:

For the first fruit variety that you pick you have 7 possible choices.
For the second fruit you also have 7 choices, any one of which can be paired with whatever was chosen for the first fruit . That is, the choices are independent. Hence the total number of combinations for choosing flavor combinations for two fruits is 7 x 7 = 49.

Now, can you extend this reasoning to determine how many combinations you can have with three fruits? Let us know what you come up with.

I got 147 different possible ways to mix and match.

I hope that's right!

Fruit 1's flavors + Fruit 2's flavors:

(1)1 2(1) 3(1) 4(1) 5(1) 6(1) 7(1)
(2)2 2(2) 3(2) 4(2) 5(2) 6(2) 7(2)
(3)3 2(3) 3(3) 4(3) 5(3) 6(3) 7(3)
4(4) 2(4) 3(4) 4(4) 5(4) 6(4) 7(4)
5(5) 2(5) 3(5) 4(5) 5(5) 6(5) 7(4)
6(6) 2(6) 3(6) 4(6) 5(6) 6(6) 7(6)
7(7) 2(7) 3(7) 4(7) 5(7) 6(7) 7(7)

Above is all of fruit 1's flavors and fruit 2's flavors mixed and matched. Added up, all those combinations equal 49.

Now times 49 by 3 and you get Fruit 2 and Fruit 3's combination and Fruit 3 and Fruit 1's combination.

Quote:

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Originally Posted by bEaUtIfUlbRuNeTtE

Above is all of fruit 1's flavors and fruit 2's flavors mixed and matched. Added up, all those combinations equal 49.

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So far so good...

Quote:

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Originally Posted by bEaUtIfUlbRuNeTtE

Now times 49 by 3 and you get Fruit 2 and Fruit 3's combination and Fruit 3 and Fruit 1's combination.

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Wrong answer - try again! Hint - for each of the Fruit 1&2 combinatons there are another 7 choices for Fruit 3.

OHHH so with fruit 1 & 2 combined we must now add fruit 3's flavors as well?

Oui! You messed me up ebaines! Hehe and I thought I had it.

One moment while I figure this out...

Might take more than a minute. Hope you got time!

Wait a moment, how many flavors are we mixing all together? 2 or 3?

196?

AGHH!

49x7=343

I hope I'm right!

Don't know how you got 196.

You wrote out all the combinations for fruit 1 and 2, and got 49. For every one of those 49 there are 7 possible chices for Fruit 3. For example, if Fruit 1 & 2 are 1 and 1, then with fruit 3 thrown in you can have 7 possible combinatoins: 111, 112, 113, 114, 115, 116, and 117. This is truew for every one of the 49 sets. Hence the answer is 49 x 7 = 343.

By the way, in all this I am assuming thathe 3 fruits each have 7 different flavors. The OP may have meant something else. If what was intended is that one picks 3 fruits out of a bowl of 7 different fruits and mixes them, the answer involves the combinaton of 7 items taken 3 at a time, or 7C3 = 35. Unfortunately, as written by the OP it's hard to tell just what is being asked...

Hey I got it right!

Well the third time I did.

I got 196 by adding 49 to my original answer which was 147. Clearly that wasn't right!

Gentlemen and Ladies,

Any time you encounter a combination you must consider all possibilities that is why this needs to be taken to the 7th power of three, which in turn gives you 2187 possible combinations.

Example: if the first fruit had banana, coconut, strawberry, peach, pear, blue berry, black berry,

This is just one of the fruits you could have,
Banana Coconut, Banana Strawberry, Banana Peach, Banana Blueberry, Banana pear, coconut strawberry, coconut peach, coconut pear, coconut blueberry, coconut Black Berry, strawberry peach, strawberry pear, strawberry blue berry, strawberry black berry, so on and so forth. I think you are getting my drift.

Have fun

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Originally Posted by infoby

this needs to be taken to the 7th power of three, which in turn gives you 2187 possible combinations.

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Sorry, this is incorrect.

1. The number of possible combinations of 7 items taken as a group of 3 is , not . See earlier postings. So 343 is the correct answer if a combination such as banana-peach-pear is considered to be different from peach-banana-pear, and if combinations such as banana-banana-banana are allowed.

2. In the examples of combinations you gave you seem to exclude any duplications of the same fruit (i.e. no banana-banana-banana), and you also seem to avoid repeats -that is, if you have banana-peach-pear then you wouldn't also include peach-banana-pear. If that's how you interpret the question, then the number of different combinations you can have is , which is calculated as: 7*6*5/(3*2*1) = 35.

In any event, the OP has not posted back with a clarification of the problem, so we're just guessing as to what was actually meant. But 2187 is definitely not the correct answer.

Quote:

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Originally Posted by bEaUtIfUlbRuNeTtE

AGHH!

49x7=343

I hope I'm right!

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Lol your funny

Why thank you britster!