What is the value of 10 ! /7 !​ ?

Explanation

Step 1: Expand the factorials

First, we expand the factorial expressions for both 10! and 7!

The factorial of a number n is defined as the product of all positive integers less than or equal to n, i.e., n!=nx (n-1)x ....... 1

Thus, we can write 10!=10 x 9x 8x7x6x5x4x3x2x1

We can also express 10! in terms of 7! as 10!= 10x9x8x7

Step 2: Simplify the expression

Next, we substitute the expanded form of1 0! into the original expression:

10!/7!= 10x9x8x7!/ 7!

We can cancel out the common term 7! from both the numerator and the denominator:

10!/7!= 10x9x8

Step 3: Calculate the final value

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