Exam2_301

Exam2_301 - Permutation P(n,r)=r-permutation of n distinct...

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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
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Exam2_301 - Permutation P(n,r)=r-permutation of n distinct...

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