urgent maths help plz!!!!!!!!!!!!!!! (1 Viewer)

[super.muppy]

i need help with this question (9.2 question 11-from Mathscape 10 (5.3) extension) (probability topic)

a new house is bought and the builder offers colours. the walls can b cream, light blue or green, and the ceilings vivid white or off-white. Different clours may b used for each room but only one clour for the cieling and one clour for the walls can b used in any single room. The house consists of four rooms; living room, kitchen, bedroom and bathroom. It is all so confusing dat the new owner of the house makes random selections for each room.

a) What is the number of posible colour schemes for the new house?
b) What is the probability of:

i) the beroom has cream walls and a vivid white setting?
ii)the living room and the bedroom have the same clour schemes?
iii)no cieling is off white?
iv) all the walls are of the same colour?
v) at least 2 rooms hav identical clour schemes?

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Giv answers plus working out
i noe dat dis is long but if u can do at least one question i will b very grateful
thanx

 

[super.muppy]

somebody help me
plz

 

[monesh]

ask your teacher or whenever i need a math problem solved i just go to this website and post the question. They reply with the full working out.

http://mathforum.org/library/drmath/sets/high_perms_combs.html

 

[lolokay]

a) 2^4 ways for the ceilings, 3^4 for the walls
total = 2^4*3^4 = 1296

b) i) 1/3 *1/2 = 1/6
ii) 6 different combiantions per room, so 1/6
iii) no off white, therefore all vivid white
this can be done in 1 way, but the ceilings can be painted in 2^4 = 16 ways
so 1/16
iv) all walls the same colour can be done in -3 ways-, out of a possible 3^4 = 81
so 3/81=1/27
v) P(at least 2 the same) = 1 - P(all different)
P(all different) = 6*5*4*3/1296 = 5/18
so P(at least 2 the same) = 13/18

 

[super.muppy]

thanx alot