Answer:
a) 332640 ways
b) 462 ways
Step-by-step explanation:
Order:
If the order of the choices matters, we use the permutations formula. If they do not matter, we use the combinations formula.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
6 objects, from a set of 11.
a) Order matters, so permutation.
[tex]P_{(11,6)} = \frac{11!}{(11-6)!} = 332640[/tex]
b) Order does not matter, so combinations.
[tex]C_{11,6} = \frac{11!}{6!(11-6)!} = 462[/tex]
