# A bag has 4 marbles purple, green, blue and red. Adam pulls out 3 marbles w/o looking. How many different combinations of 3 colors are possible?(note 4th grade math no complicated formulas) The...

A bag has 4 marbles purple, green, blue and red. Adam pulls out 3 marbles w/o looking. How many different combinations of 3 colors are possible?

(note 4th grade math no complicated formulas) The one thing that is confusion is i do not know if red, blue, purple is the same as purple, blue, red..I would assume it is the same and order does not matter

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### 5 Answers

What you are doing here is (as your tag says) combinations. This is as opposed to permutations. The difference is that, with combinations, order doesn't matter (Adam is grabbing them all at once, not one at a time). Permutations are when he grabs them one at a time.

The correct answer for your question is four -- there should be four different combinations of three marbles that Adam could grab. The possibilities are

- purple, blue, green
- purple, green, red
- purple, blue, red
- blue, red, green

Any other combination would be a repeat (like blue, red, purple), just in a different order.

When the order in which the marbles of different colours are pulled out is not considered, then the question can be answered very simply by modifying it the different possibilities regarding the fourth marble that is left in the bag after three marbles have been pulled out of the bag. This is because just by looking at the the fourth marble, we can tell which other three marbles have been pulled out.

There are just 4 different possibilities of the fourth marble left in the bag - 1) purple, 2) green, 3) blue and 4) red. Corresponding to this there are four combinations of three marbles pulled out. These are:

1) green, blue and red,

2) purple, blue and red,

3) purple, green and red,

4) purple, green, and blue.

In combinations , the order is to be ignored. In permutations orders or arrangements are to be considered.

From four marbles , green, blue,red and adam, how many combunatuions are possible? The number of combinations of three is as mmany as how many possibility of remaining one you leave when you choose 3. Possiblities are:

a) Choosing the 3 other than green or

b) Choosing the 3 other than blue or

c) Choosing the 3 other than red or

d) Choosing the three other than adam.

Thus it is 4 posible ways. Or 4C3 = 4.

If you are interested in permutation or arranging the 3 things chosen combination, the order also counts. Then for each of the 4 choices further arranging 3! whitin each choice makes the number of permutations 4P3 = 4*3! =24.

Order does not matter.