a pharmacist uses 5 separate weights: 1g, 2g,4g,8g and 16g. If the pharmacist can combine these weights to create a new weight, how many different weights are possible?

the 1 g weight can be used in 2 ways, either take it or don't take

the 2g weight can be used in 2 ways, either take it or don't take it
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so there are 2x2x2x2x2 ways to use the weights or 32
but that includes the case where none of the weights are used and all of the weights are used.

So depending on the wording of the question I would subtract 1 for no weights at all,
so there would be 31 ways.

Well, it seems like our pharmacist has quite the weighty situation on their hands. Let's do some math and weigh out the possibilities.

With the 5 separate weights of 1g, 2g, 4g, 8g, and 16g, we can start combining them to create new weights. Each weight can be either included or not included, giving us two options for each weight.

Using the power of multiplication, we know that the total number of possible combinations is found by multiplying the number of options for each weight: 2 x 2 x 2 x 2 x 2 = 32.

So, our talented pharmacist can create 32 different weights by cleverly combining the 5 separate weights! That's weighty impressive, don't you think?

To calculate the number of different weights that can be created using the 5 separate weights of 1g, 2g, 4g, 8g, and 16g, we can use the concept of combinations.

The total number of combinations possible when selecting from 5 weights is given by the formula:
Number of combinations = 2^n
where n is the number of elements (weights) being combined.

In this case, there are 5 weights, so n = 5.
Number of combinations = 2^5 = 32

Therefore, there are 32 different weights that can be created by combining the 5 separate weights of 1g, 2g, 4g, 8g, and 16g.

To find out how many different weights are possible, we can use the concept of binary numbers. Each weight can be represented as a power of 2 because we have weights of 1g, 2g, 4g, 8g, and 16g, which are all powers of 2.

We can assign each weight a numerical value as follows:
1g = 2^0 = 1
2g = 2^1 = 2
4g = 2^2 = 4
8g = 2^3 = 8
16g = 2^4 = 16

To find all possible combinations, we can use binary representation. Each weight can either be present (1) or not present (0) in a combination.

Since we have 5 separate weights, there are two possibilities for each weight (presence or absence). So, the total number of combinations is 2^5, which is equal to 32.

Therefore, there are 32 different weights that can be created by combining these 5 separate weights.