\(\frac{10 !}{7 !}\) is equal to:

720

Explanation

10! is 10 factorial, which is defined as \(10 !=10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\) .

7! is 7 factorial, which is defined as \( 7!{\rm{ }} = {\rm{7}} \times {\rm{6}} \times {\rm{5}} \times {\rm{4}} \times {\rm{3}} \times {\rm{2 }} \times {\rm{1}}\).

When 10! is divided by 7!, the common terms 7, 6, 5, 4, 3, 2, and 1 in the numerator and denominator get cancelled. So \(\frac{10 !}{7 !}=10 \times 9 \times 8=720\)

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