For the following exercises, determine whether to use the Addition Principle ...How many ways are there to construct a string of 3 digits if numbers can be repeated?

For the following exercises, determine whether to use the Addition Principle or the Multiplication Principle. Then perform the calculations.

How many ways are there to construct a string of 3 digits if numbers can be repeated?

Expert Solution

Consider to construct a string of 3 digits if numbers can be repeated.

As the hundred’s place cannot have the ‘0’ digit, there are ‘9’ options for hundred’s place. (It can be any digit from 1 to 9).

The tens digit can have any digit from 0 to 9, there are ‘10’ options for tens place.

The ones digit can have any digit from 0 to 9, there are ‘10’ options for ones place.

As three digits are to be chosen, one for three places, “Multiplication Principle” will be used.

Multiplication Principle,

“If one event can occur in m ways and a second event with no common outcomes can occur in n ways after the first event has occurred, then the two events can occur in m × n ways.”

Using the multiplication principle,

The total number of possible three digits string will be,

9 × 10 × 10 = 900

The total number of possible three digits string will be,

9 × 10 × 10 = 900

Umair answered 1 year ago

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