Evaluate the expression.
11!
6!
4!
2!
3!
1!
11 factorial = 11! = 11 * 10 * 9 … * 3 * 2 * 1
Same process for other factorials.
To evaluate the given expressions, let's calculate the factorial values first.
Factorial is denoted by "!". It means multiplying all positive integers from 1 up to the given number.
So, here are the factorial values for each expression:
11! = 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 39,916,800
6! = 6 × 5 × 4 × 3 × 2 × 1 = 720
4! = 4 × 3 × 2 × 1 = 24
2! = 2 × 1 = 2
3! = 3 × 2 × 1 = 6
1! = 1
Now let's evaluate the expressions step-by-step:
11! / 6!
= 39,916,800 / 720
= 55,440
4! / 2!
= 24 / 2
= 12
3! / 1!
= 6 / 1
= 6
So, the evaluations of the expressions are:
11! / 6! = 55,440
4! / 2! = 12
3! / 1! = 6
To evaluate the given expressions, we need to compute the factorials.
Factorial is denoted by an exclamation mark (!) and it represents the product of all positive integers less than or equal to a given number.
Let's calculate the factorials one by one:
1. 11!:
To compute 11!, we multiply all the positive integers starting from 11 and going down to 1:
11! = 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 39,916,800
2. 6!:
Similarly, for 6!, we multiply all the positive integers from 6 down to 1:
6! = 6 × 5 × 4 × 3 × 2 × 1 = 720
3. 4!:
For 4!, we multiply all positive integers from 4 down to 1:
4! = 4 × 3 × 2 × 1 = 24
4. 2!:
And for 2!, we multiply 2 and 1:
2! = 2 × 1 = 2
5. 3!:
Lastly, for 3!, we multiply 3, 2, and 1:
3! = 3 × 2 × 1 = 6
So, the evaluated expressions are:
11!/6! = 39,916,800/720 = 55,444
4!/2! = 24/2 = 12
3!/1! = 6/1 = 6