Answer:
840 possible permutations of 7 objects 4 ways.
Explanation:
Good question! I had to look it up, but I found a formula by searching on some of the key words. Here's the general equation:
P = n!
(n -r)!
Where:
- P is the number of possible permutations
- n = the number of things
- r = the number of ways they can be arranged
- ! is the "factorial function."
Do you know factorial? It simply means to multiply a number by all the numbers lower than it.
So in this question:
So:
P = 7!
(7-4)!
7! means: 7·6·5·4·3·2·1
And with (7-4)! you get to do the math inside and then take the factorial, so it's simply 3!, or 3·2·1
But notice that "3·2·1" is in the numerator and denominator. So 3! cancels out, like common factors in a fraction. So we can rewrite it like this:
P = 7·6·5·4·3!
3!
Do you see how I wrote 3! so I didn't have to write out 3·2·1? I did that so it looks like the (7-4)! = 3! term in the denominator.
Those cancel each other, and we're left with:
P = 7·6·5·4 = 840 permutations of 7 objects 4 ways.