WEBVTT
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Evaluate eight P five.
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The notation in this question tells us that we are dealing with permutations.
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We know that a permutation is an arrangement of a collection of items.
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When dealing with permutations, order matters and repetition is not allowed.
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We can calculate the number of permutations using the formula π factorial divided by π minus π factorial.
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This is the number of ways we can select π elements from a collection of π elements.
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In this question, we need to calculate the number of ways we can select five elements from a group of eight elements without repetition and where order matters.
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Substituting in our values, we have eight factorial divided by eight minus five factorial.
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As eight minus five is equal to three, this simplifies to eight factorial divided by three factorial.
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We recall that π factorial is equal to π multiplied by π minus one factorial.
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This means that we can rewrite the numerator as eight multiplied by seven multiplied by six multiplied by five multiplied by four multiplied by three factorial.
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We can then divide the numerator and denominator by three factorial.
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Multiplying the five integers from eight to four inclusive gives us 6720.
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There are 6720 ways we can select five items from a group of eight items.
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It is important to note that there are different notations that can be used in these type of questions, some of which are shown.
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We could also have used a scientific calculator to work out the answer.
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We simply type the π value followed by the πPπ button and then the π value.
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Pressing βequalsβ will then give us our answer.
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In this case, eight P five is equal to 6720.