SOLUTION: 18) In a box there are 8 red and 6 blue markers. How many ways can you select 3 markers if: (a) exactly 1 red is selected? (b) no more than 2 blue are selected? (c) there are mo

Algebra ->  Permutations -> SOLUTION: 18) In a box there are 8 red and 6 blue markers. How many ways can you select 3 markers if: (a) exactly 1 red is selected? (b) no more than 2 blue are selected? (c) there are mo      Log On


   



Question 1018797: 18) In a box there are 8 red and 6 blue markers. How many ways can you select 3 markers if:
(a) exactly 1 red is selected?
(b) no more than 2 blue are selected?
(c) there are more blue than red selected?
I'm not sure where to begin can you please guide me through?

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
8 ways to select one red.
6C2 ways to select 2 blue
that is 15.
numbering the blues 1 through 6
12
13
14
15
16
23
24
25
26
34
35
36
45
46
56
So the number of ways are 8*15=120
no more than two blue mean 15 ways for 2+6 ways for 1+the number of ways one can select 3 from 8 red (0 blue). That is 8C3 or 56 ways, so the total is 15+6+56=77 ways.
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more blue than red.
3 blue and 0 red. That is 6C3=20 ways. 6C3 is the number of ways one can select 3 items from 6. It si 6!/3!/3!, or 6*5*4*3!/3!3!
2 blue and 1 red. That is 6C2*8=120 ways and the total is 140 ways.