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Using the letters in the word INNOVATIVE,find the number of permutations that can be formed using 4 letters at a time.Show your work or explain how you got your answer

Sagot :

Given:-

[tex]INNOVATIVE[/tex]

To find the number of permutations that can be formed using 4 letters at a time.

Since there are 10 letters and using 4 letters form permutation.

So now we use the formula,

[tex]10p_4[/tex]

So now we simplify. so we get,

[tex]10p_4=\frac{10!}{(10-6)!}=\frac{10!}{4!}=\frac{10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{1\times2\times3\times4}[/tex]

So now we simplify,

[tex]\frac{10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{1\times2\times3\times4}=10\times9\times8\times7\times6\times5[/tex]

So now we get,

[tex]10\times9\times8\times7\times6\times5=151200[/tex]

So now we get the solution as 151200

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