Counting Flashcards
And
Multiply
Or
Add
FCP
N=n1n2n3; think of slots
Order
Factorials
Restrictions
1) Start with most rest; once that is decided= how many are left
Number of arrangements that do not obey restrictions:NOT
n!=R+Q=> total=obey-not obey
Symmetry
For each order with R before L; there is an arrangement in which L before R; therefore: total number of arrangements/2
Identical Items
4 books and 3 dict; if all were different 7!; if 4 books order was constant and the three dict were treated different then thay could be arranged in 3! order; but we are double counting so 7!/3! or n!/b!c!d! (multiple identical items);
Sometimes when order doesnt matter; 3 distinct set of marbles
All three same color, two and 1, or 1,1,1
Repetitions (normal counting)
Have to divide the total number: 20 people how many handshakes will occur: 20*19/2 because you are counting twice A shakes hands with B and B shakes hands with A
From a set of 10 different items Lisa picks 3, how many different sets of 3 can she pick?
Order DOES NOT matter so 1098; because here you are assuming order; you are counting 3! too many times so arrangements is 1098/3!
***DOES ORDER MATTER?
if yes FCP if no combination
nCr=
nc1=n; 10C4=10C6; nCr=nC(n-r); n!/(r!)(n-r!)
nCr logic
FCP and then dividing byr! to eliminate repition
Does order matter?
When you look at the answer: are the results affected if you switch the answers around:: results oriented
