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Q: How many ways can 2 pens be chosen from 4 pens?
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Continue Learning about Basic Math

How many different ways can you write a fraction that has a numerator of 2 as a sum of fractions?

Infinitely many ways, since if you have found one way then take one of the fractions and replace it by an equivalent fraction. Repeat for ever.


How many different ways can 40 be written as a sum of 2 positive prime numbers?

Three ways. 3 + 37 11 + 29 17 + 23


How many backpacks out of 38 contained none of the three writing instruments?

First, I would like to say that the whole question is not here. The question states: upon examining the contents of 38 backpacks, it was found that 23 contained a black pen, 27 contained a blue pen, and 21 contained a pencil, 15 contained both a black pen and a blue pen, 12 contained both a black pen and a pencil, 18 contained both a blue pen and a pencil and 10 contained all three items. How many backpacks contained none of the three writing instruments? OK I will explain this the best I can! Starting out, their are 10 backpacks that contain all the items. 12 contained both a black and blue pen. You would subtract 10 from 12; therefore there are 2 backpacks that contain only black and blue pens. 18 contain both a blue pen and a pencil. subtract 10 from 18 and you get 8. 15 contained both a black pen and a blue pen. You would subtract 10 from 15 and you get 5. There are 23 with black pens. So you would do 23 - (5+10+2)= 6. There are 6 backpacks that contain only black pens. There are 27 that contain blue pens. So you would do 27 - (5+10+8) = 4. There are 4 backpacks that contain only blue pens. There are 21 backpacks that contain a pencil. You would do 21 - (2+10+8) = 1. All together, there a 6 that contain only black pens, 5 that contain only black and blue pens, 4 that contain only blue pens, 10 that contain all three items, 2 that contain only black pens and pencils, 8 that contains only blue pens and pencils, and 1 that contains only 1 pencil. So you would add 6+5+4+10+8+2+1= 36. There are 38 backpacks, so you would subtract 36 from 38. There are 2 backpacks that contain none of the three writing instruments. Ashfords quiz says this is right.


How do you get 72 but with only prime numbers?

there are many (infinite) ways but just one is 72=2*(31+5)


How many ways can 24 be written as the sum of 2 different prime numbers?

24 = 11 + 13 = 5 + 19