math problem 3?

Question

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.

Answer 1

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!

Answer 2

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