Hi my question is find the value of the following.
6! 8! over 9! 5!
If your answer is not an integer, write it as an exact fraction.
Thank you so much. I have no idea how to do it.
quick way:
on your calculator find a key usually labeled n!
(on mine to find 6!, I keystroke like this:
6
2ndF
n!
=
to get 720
so for (6!8!)/(9!5!) you should get 2/3 or .6666...
or
use the definitions:
also recall that the concept that 9! = 9x8!
since this suits our expression nicely we can say
(6!8!)/(9!5!)
= (6x5! 8!)/(9x8! 5!) , now cancel the 8! and the 5! )
= 6/9 = 2/3
Thank you very much Reiny
To find the value of the given expression:
1. Start by simplifying each factorial separately. Remember, n! means the product of all positive integers up to n.
a) 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720
b) 8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40,320
c) 9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 362,880
d) 5! = 5 × 4 × 3 × 2 × 1 = 120
2. Substitute the simplified factorials back into the original expression:
6! * 8! / 9! * 5!
= (720 * 40,320) / (362,880 * 120)
3. Simplify the expression further:
= 29,030,400 / 43,545,600
4. Check if the result is an integer or a fraction:
Since the numerator (29,030,400) and denominator (43,545,600) cannot be simplified further, we can leave the answer as a fraction: 29,030,400 / 43,545,600.