WEBVTT
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Evaluate seven permute four divided by five permute two.
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So to evaluate this, we need to work out how we actually find out the value of something like seven permute four.
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Well, we actually have a general formula that tells us that đť‘› permute đť‘ź is equal to đť‘› factorial over đť‘› minus đť‘ź factorial.
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So with this formula, itâ€™s worth reminding yourself what factorial is.
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And the factorial shown here â€” we have five factorial â€” is five multiplied by four multiplied by three multiplied by two multiplied by one.
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And to find any factorial, all we do is actually multiply all the positive integers that are less than or equal to the number which is in the factorial.
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Okay, so now we know this.
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Letâ€™s evaluate our seven permute four divided by five permute two.
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First of all, Iâ€™m actually gonna find seven permute four.
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And using our general formula is gonna be equal to seven factorial divided by seven minus four factorial which is gonna be equal to seven factorial over three factorial.
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So now, weâ€™re just gonna show what this means.
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It means weâ€™d have seven multiplied by six multiplied by five multiplied by four multiplied by three multiplied by two multiplied by one cause thatâ€™s our seven factorial then divided by three multiplied by two multiplied by one.
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Well, then, our three factorial actually cancels out.
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So we can actually remove three multiplied by two multiplied by one from the numerator and the denominator.
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So then, weâ€™re left with seven multiplied by six multiplied by five multiplied by four which gives us a value of 840.
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So great, weâ€™ve now found the value of seven permute four.
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Letâ€™s move on and find the value of five permute two.
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Well, five permute two is equal to five factorial over five minus two factorial.
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And again, we got this from our general formula which is gonna be equal to five factorial over three factorial.
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So again, we just put in this extra step to show you whatâ€™s happening.
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So weâ€™ve got five multiplied by four multiplied by three multiplied by two multiplied by one divided by three multiplied by two multiplied by one.
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Again, our three factorial cancels.
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So weâ€™re just left with five multiplied by four.
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So therefore, we have a value of five permute two of 20.
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Okay, great, so now, we can actually move on to the final stage which is to evaluate our starting question.
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So therefore, we can say that seven permute four over five permute two is gonna be equal to 840 divided by 20 which is gonna give us a final answer of 42.