Determine the following:
a) The number of combinations of 7 out of 10 items.
b) The number of permutations of 5 out of 9 items.
c) The number of combinations of 4 out of 7 items.
d) The number of permutations of 6 out of 6 items.
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I have a friend who is taking statistics and I help her sometimes...she had these a few days ago. Here are the equations:
The number of combinations of n distinct objects taken r at a time is:
C = n! / (r! (n-r)!)
so, for (a) n=10 and r=7
The number of permutations of n distinct objects taken r at a time is:
P = n! / (n-r)!
so, for (b) n=9 and r=5
I hope that helps. Good luck!
A few theorems first:
The number of combinations of n distinct objects taken r at a time (nCr) is given by:
n! / r! (n-r)!
The number of permutation of n distinct objects taken r at a time (nPr) is given by:
n! / (n-r)!
That is all you need to answer these questions:
a) 10C7 = 10! / 7! (10-7)! = 10! / 7! 3! = 120
b) 9P5 = 9! / (9-5)! = 9! / 4! = 15,120
c) 7C4 = 7! /4! (7-4)! = 7! / 4! 3! = 35
d) 6P6 = 6!/ (6-6)! = 6! / 1 = 720