Question

10!/6!

Answer 1

The exclamation mark means factorial. Are you familiar with factorial numbers?

Answer 2

\(\LARGE\color{blue}{ \bf \frac{10!}{6!}=\frac{6! \times 7 \times 8 \times 9 \times 10}{6!} }\)

Answer 3

No :/

Answer 4

A factorial number is a product of numbers.
Factorial is used only with non-negative integers.
For example, 5! means 5 * 4 * 3 * 2 * 1

Answer 5

Thank You Guys

Answer 6

YW

Answer 7

If you are given only a factorial number, and you need to evaluate it, you simply multiply it out.

For example,

6! = 6 * 5 * 4 * 3 * 2 * 1 = 720

On the other hand, if you have a fraction of factorial numbers, very often you can do what Solomon did above. You expand the factorial to show what the product is, and then you can reduce the fraction before multiplying it out. Then you have less of a multiplication or division to do.

For example,

\(\dfrac{12!}{4!}\)

\( = \dfrac{12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4!}{4!}\)

\( = \dfrac{12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times \cancel{4!}}{\cancel{4!}}\)

\( = 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \)

\(= 19,958,400\)

Answer 8

Isn't that the answer? o:

Answer 9

Yes, the answer is 5040, but it can be done with less work.

\(\dfrac{10!}{6!}\)

\( = \dfrac{10 \times 9 \times 8 \times 7 \times 6!}{6!} \)

\( = \dfrac{10 \times 9 \times 8 \times 7 \times \cancel{6!}}{\cancel{6!}~~~1} \)

\(= 10 \times 9 \times 8 \times 7\)

\(= 5040\)