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How many different positive three-digit integers can be formed if the three digits 3, 4, and 5 must be used in each of the integers?
  • a)
    6
  • b)
    8
  • c)
    12
  • d)
    15
  • e)
    24
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
How many different positive three-digit integers can be formed if the ...
The correct answer is a. To solve, write out every possible three-digit integer: 345, 354, 435, 453, 534, and 543; six different positive three-digit numbers can be formed, answer choice a.
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How many different positive three-digit integers can be formed if the ...
Explanation:

Arrangement of Digits:
- Since the three digits 3, 4, and 5 must be used in each of the integers, the arrangement of these digits will result in 3! = 6 possible combinations.

Placement of the Remaining Digits:
- After placing the digits 3, 4, and 5, there are 3 remaining digits (0, 1, 2, 6, 7, 8, 9) that can be placed in the hundreds, tens, and units place.
- For each of the 6 possible arrangements of 3, 4, and 5, there are 3 options for placing the hundreds digit, 2 options for placing the tens digit, and 1 option for placing the units digit.
- Therefore, the total number of different positive three-digit integers that can be formed is 6 * 3 * 2 * 1 = 36.
- However, since we are only considering three-digit integers, the hundreds digit cannot be 0. So, we subtract the 6 numbers where the hundreds digit is 0.
- Therefore, the total number of valid positive three-digit integers is 36 - 6 = 30.

Conclusion:
- The number of different positive three-digit integers that can be formed if the digits 3, 4, and 5 must be used in each of the integers is 30.
- The correct answer is option 'A' (6).
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Magnets and electric charges show certain similarities. For example, both magnets and electric charges can exert a force on their surroundings. This force, when produced by a magnet, is called a magnetic field. When it is produced by an electric charge, the force is called an electric field. It has been observed that the strength of both magnetic fields and electric fields is inversely proportional to the square of the distance between a magnet or an electric charge and the objects that they affect.Below, three scientists debate the relationship between electricity and magnetism.Scientist 1:Electricity and magnetism are two different phenomena. Materials such as iron, cobalt, and nickel contain magnetic domains: tiny regions of magnetism, each with two poles. Normally, the domains have a random orientation and are not aligned, so the magnetism of some domains cancels out that of other domains; however, in magnets, domains line up in the same direction, creating the two poles of the magnet and causing magnetic behavior.In contrast, electricity is a moving electric charge which is caused by the flow of electrons through a material. Electrons flow through a material from a region of higher potential (more negative charg e) to a region of lower potential (more positive charge). We can measure this flow of electrons as current, which refers to the amount of charge transferred over a period of time.Scientist 2:Electricity and magnetism are similar phenomena; however, one cannot be reduced to the other. Electricity involves two types of charges: positive and negative charge. Though electricity can occur in a moving form (in the form of current, or an electric charge moving through a wire), it can also occur in a static form. Static electricity involves no moving charge. Instead, objects can have a net excess of positive charge or a net excess of negative charge—because of having lost or gained electrons, respectively. When two static positive electric charges or two static negative electric charges are brought close together, they repel each other. However, when a positive and a negative static charge are brought together, they attract each other.Similarly, all magnets have two poles. Magnetic poles that are alike repel each other, while dissimilar magnetic poles attract each other. Magnets and static electric charges are alike in that they both show attraction and repulsion in similar circumstances. However, while isolated static electric charges occur in nature, there are no single, isolated magnetic poles. All magnets have two poles, which cannot be dissociated from each other.Scientist 3:Electricity and magnetism are two aspects of the same phenomenon. A moving flow of electrons creates a magnetic field around it. Thus, wherever an electric current exists, a magnetic field will also exist. The magnetic field created by an electric current is perpendicular to the electric currents direction of flow.Additionally, a magnetic field can induce an electric current. This can happen when a wire is moved across a magnetic field, or when a magnetic field is moved near a conductive wire. Because magnetic fields can produce electric fields and electric fields can produce magnetic fields, we can understand electricity and magnetism as parts of one phenomenon: electromagnetism.Q. Which of the following would be an example of electricity according to Scientist 2, but not according to Scientist 1?

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How many different positive three-digit integers can be formed if the three digits 3, 4, and 5 must be used in each of the integers?a)6b)8c)12d)15e)24Correct answer is option 'A'. Can you explain this answer?
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