SOLUTION: Eight cards are selected with replacment from a standard pack of 52 playing cards, with 12 picture cards, 20 odd cards and 20 even cards. How many sequences of 8 are possible, that

Algebra ->  Permutations -> SOLUTION: Eight cards are selected with replacment from a standard pack of 52 playing cards, with 12 picture cards, 20 odd cards and 20 even cards. How many sequences of 8 are possible, that      Log On


   

Question 13331: Eight cards are selected with replacment from a standard pack of 52 playing cards, with 12 picture cards, 20 odd cards and 20 even cards. How many sequences of 8 are possible, that include 3 picture cards, 3 odd cards and 2 even cards,
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
[quote] Eight cards are selected with replacment from a standard pack of 52 playing cards, with 12 picture cards, 20 odd cards and 20 even cards. How many sequences of 8 are possible, that include 3 picture cards, 3 odd cards and 2 even cards [/quote]
Sol:There are C(12,3) sets of picture cards, C(20,3) sets odd cards ,
C(20,2) sets of even cards.
Since we have to consider the sequence of 8 cards in order,totally,
there are 8!*C(12,3)*C(20,3)*C(20,2) (leave like that or)
= 8!*2*11*10*20*19*3*10*19
=1.92133E+12 (I use Excel)
Kenny