A combination is an set of objects selected without respect to order or arrangement.
n Cr = n!/(n-r)! r!
Think of the letters a,b,c,d. I want to pick three
Permutations
abc abd acd bcd
acb adb adc bdc
bac bad cad cbd
bca bda cda cdb
cab dab dac dbc
cba dba dca dcb
Combinations
abc abd acd bcd
acbadbadcbdcbacbadcadcbdbcabdacdacdbcabdabdacdbccbadbadcadcb
Examples:
Tina must select and answer four of five essay questions on a test. How many ways can she do so?
When visiting New York City, the Nygens want to attend 3 out of ten plays. How many ways can they do so?
Matthew has 10 shirts in his closet and must select 4 to take with him on vacation. How many ways can Matthew select the shirts.
On an English test, Titio must write an essay for three of the five questions in part I and four of the six questions in part 2. How many different combinations of questions can he answer.
Sue is having a dinner party. She has 10 different bottles of red wine and 8 different bottles of white wine. She wants to select 4 bottles of red wine and 2 bottles of white wine to serve at her party. How many ways can she do this?
General Mills is testing 4 oat cereals, 5 wheat cereals and 6 rice cereals. If it plans to market 3 oat cereals, 2 wheat cereals and 2 rice cereals, how many different combinations are possible?