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How many four-digit numbers can be formed using the elements of the set one, two, three, seven, and nine?
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One way of answering this question is using the fundamental counting principle.
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This states that if there are P ways to do one thing and Q ways to do a second thing, there are P multiplied by Q ways to do both things.
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In this question, we are trying to create a four-digit number.
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There are five elements in the set, and there is no restriction on repetition.
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We can choose any one of the five elements one, two, three, seven, and nine for the first digit.
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We can also choose any one of the five elements for the second digit.
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Likewise, there are five possible choices for the third digit, and the same is true for the fourth digit.
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The total number of four-digit numbers from the set will therefore be equal to five multiplied by five multiplied by five multiplied by five.
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Five multiplied by five is equal to 25.
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And multiplying 25 by 25 gives us 625.
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There are 625 four-digit numbers that could be formed from the elements of the set one, two, three, seven, and nine.
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An alternative method here would be to use our knowledge of permutations.
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When calculating the total number of permutations with replacement, we use the formula 𝑛 to the power of 𝑟.
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In this case, the value of 𝑛 is the number of elements in the set, and the value of 𝑟 is the number of digits.
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We need to calculate five to the fourth power or five to the power of four.
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Once again, this gives us an answer of 625.