How many ways can you choose a set of 9 pencils from a selection of 10?
2 Answers
See a solution process below:
Explanation:
There are 10 choices for the first pencil.
There are 9 choices left for the second pencil
There are 8 choices left for the third pencil
and so on
Until the are 2 choices left for the ninth pencil
This means the number of ways you can choose 9 pencils from a selection of 10 is:
Explanation:
When we are asked to "choose" a number of objects from a larger set, we use combinations. This is because the order of the objects does not matter. If the order did matter, we would use permutations.
In this case, we would be choosing
In general terms, a combination is defined as:
Substituting our values in, we get
#=(10!)/(9! * 1!)#
#=(10*9!)/(9!*1)#
#=(10*cancel(9!))/(cancel(9!)*1)#
#=10#
Thus, there are