http://www.ck12.org Chapter 2. Conditional Probability
ticket. The numbers drawn simply have to be on your lottery ticket in order for you to win. You can imagine how
many possible combinations of numbers exist, which is why your odds of winning are so small!
Combinationsare arrangements of objectswithoutregard to order and without repetition, selected from a distinct
number of objects. A combination ofnobjects takenrat a time(nCr)can be calculated using the formula:
nCr=n!
r!(n−r)!Example A
Evaluate: 7 C 2.
7 C 2 =
7!
2!( 7 − 2 )!
7 C 2 =
7!
2!( 5 )!
7 C 2 =
7 × 6 × 5 × 4 × 3 × 2 × 1
( 2 × 1 )( 5 × 4 × 3 × 2 × 1 )
7 C 2 =
5 , 040
( 2 )( 120 )
7 C 2 =
5 , 040
240
7 C 2 =^21
Example B
In how many ways can 3 desserts be chosen in any order from a menu of 10?
There are 10 menu items(n= 10 ), and you are choosing 3 desserts in any order(r= 3 ).