Permutation: P(n,r)=r-permutation of n distinct objects is an arrangement using r of the n objects.
ORDER
MATTERS: P(n,r) = n!/(n-r)!
Combination: C(n,r) A r-combination of n distinct objects is an unordered selection of r out of n objects.
C(n,r)
=n!/{(n-r)!r!)
C(n,r)=C(n,n-r)
P(n,r)=C(n,r)*r!
How many ways are there
to form a sequence of 10
letters from 4as, 4bs, 4cs, and 4ds if each letter must appear at least twice?
Aa bb cc dd aa
4 cases
P(10; 4, 2, 2, 2) = 18,900 limited repetition + ordered
aa bb cc dd ab
C(4,2) have 4 letter choose 2diff =6 cases
P(10; 3, 3, 2, 2) = 25,200
= we have 10 total
letter, 3 of 2 types of letter, 2 of 2 other types limited repetition + ordered
A: 4 ×18,900+ 6×25,200 =
226,800
How many ways are there to pick exactly 10 balls from a pile of red, blue and purple balls, if there must be at
most 5 red balls? 10 balls from 3 types c(10+3-1,10)=66 At least 6=At most 5 . At least 6 is
C(4+3-1,4) This is the leftover 3=types 1 in formula, 4 is leftover balls.
Six cups of diff flavor ice cream: Distribute to 3 kids: r distinct objects to 3 kids: n^r
Distribute with restriction, 2 to J, 3toM 1 to Rose: P(r:r1,r2,rn) ri objects go in box i.
Distribute 6 cups of identical object to 3 things: C(r+n-1, r)= (r+n-1)!/r!(n-1)!
*How manyways if 20 diplomats must be assigned to each country.100 total diff diplomats 5 countries: Distinct
distribution with repetition: P(100:20,20,20,20,20) 20 for 5 country , 100 total distinct items(diplomats):::*Bridge,
52 cards 13 to each player, possibility all spades: total outcomes C(52,13) only one possible outcome to get all