What is the value of 10 ! /7 ! ?
- 210
- 504
- 720
- 840
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
Finally, we multiply the remaining numbers:
10x9x8 = 90 x 8 = 720
The final result of the expression is 720
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