Question 212005: A specific brand of bike comes in two frames, for males or females. Each frame comes in a choice of three colors, red, white, and blue, and with a choice of three seats, soft, medium, and hard.
a) Use the counting principle to determine the number of different arrangements of bicycles that are possible.
b) Construct a tree diagram illustrating all the different arrangements of bicycles that are possible.
c) List the sample space.
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! Let M=male,,,F=Female,,,,frames
Let R=red,,W=white,,B=blue,,,colors
Let S=soft,,,M=medium,,,H=hard,,,construction
.
a) 2(frames) *3(colors) *3(constructions) = 18 combinations.
.
b),,,as it is hard to space without some holding device, pls ignore (.) 's
.
............................S.....................................................
..................R........M......................................................
............................H.....................................................
............................S......................................................
.........M......W........M......................................................
............................H......................................................
............................S.....................................................
..................B........M.....................................................
............................H.....................................................
............................S.....................................................
..................R........M.....................................................
............................H.....................................................
............................S.....................................................
.........F......W........M.....................................................
............................H.....................................................
............................S......................................................
..................B........M.....................................................
............................H.......................................................
PLEASE DRAW THE CONNECTING LINES
C)I'll list them, but tree shows them clearer
.
MRS,MRM,MRS,,,MWS,MWM,MWH,,,,MBS,MBM,MBH
.
FRS,FRM,FRH,,,FWS,FWM,FWH,,,,FBS,FBM,FBH
.
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