Write in terms of factorials 5 6 7 8 9 10 - Vidyadip

Question

Write in terms of factorials
$5 \times 6 \times 7 \times 8 \times 9 \times 10$

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Answer

$5 \times 6 \times 7 \times 8 \times 9 \times 10 = 10 \times 9 \times 8 \times 7 \times 6 \times 5$ Multiplying and dividing by 4!, we get
$=\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 !}{4 !}$
$=\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{4 !}$
$=\frac{10 !}{4 !}$

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