Combinactorics (1).pdf - Combinatorics Assignment Maya Dras 1 a ​How many different three-color flags(tricolors can be designed using green blue red

Combinactorics (1).pdf - Combinatorics Assignment Maya Dras...

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Combinatorics Assignment Maya Dras 1 a) How many different three-color flags (tricolors) can be designed using green, blue, red, yellow and black stripes if all three colors must be different? 5 x 4 x 3 = 60 b) How many of them contain a red stripe? Red included Red not included 5 x 4 x 3 = 60 4 x 3 x 2 = 24 =60 -24 = 36 Therefore, 36 of them contain a red stripe c) How many extra possibilities are there if the top color can be the same as the bottom color? - 5 possibilities for the top stripe - 4 possibilities for the middle stripe - the remaining 3 colors plus the top stripe color for the bottom stripe. 5 x 4 x 4 = 80 80-60= 20 , 20 different possibilities. 2) In how many ways can Prashad list his course choices? P (6,4) = 6!/(6-4)! = 6x5x4x3x2x1/2x1 = 6x5x4x3 = 360 P (4,3) = 4!/(4-3)! = 4x3x2x1/1 = 24 = 360 + 24 = 84 1
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Prashad is choosing four of six courses and three of the four courses. Courses cannot be repeated therefore we use permutations. 3a) How many different passwords are possible? 36P8 = 36!/28! = 1,220,096,908,800 b) How many are possible if the password must feature both numbers and letters?
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