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Final solutions are provided but please show the method:

A work crew for a building project is to be made up of two craftsmen and four laborers selected from a total of five craftsmen and six laborers.
a. How many different combinations are possible? (ans:150)
b. The brother of one of the craftsmen is a laborer. If the crew is selected at random, what is the probability that both brothers will be selected? (ans: 0.2667)
c.What is the probability that neither brother will be selected? (ans: 0.20)

2007-11-14 04:21:59 · 4 answers · asked by Albert A 2 in Science & Mathematics Mathematics

4 answers

a. Use the combinations formula.

Selecting k objects from n objects the formula is (n!)/[k! * (n-k)!]

Choose 2 craftsmen from 5. That would equal (5!)/(2!3!) = 120/12 = 10
Choose four laborers from 6. That would equal (6!/(4!2!) = 720/48 = 15

Multiply the number of ways to choose laborers by the number of ways to choose craftsmen. 10 * 15 = 150.

b. The brother who is a craftsman has 2 in 5 chance of being selected, being that 2 craftsmen are selected from 5. 2/5 = 0.4. The brother who is a laborer has a 4 in 6 chance of being selected. 4/6 = .6667. Multiply each brother's chances of getting selected. 0.4 * 0.6667 = 0.26667

c. The is a 3 in 5 chance that brother #1 doesn't get selected. 3/5 = 0.6 There is a 2 in 6 chance that brother #2 doesn't get selected. 2/6 = .3333
Again,multiply the respective probabilities. 0.6 * 0.3333 = 0.20

2007-11-14 04:33:34 · answer #1 · answered by SoulDawg 4 UGA 6 · 1 0

No. of combinations = 5C2 x 6C2
= (5x4)/2 x (6x5)/2
= 10 x 15
= 150

Probability that brothers are selected = 1/5 x 1/6
= 1/30

Probability that no brother is selected = 1 - 1/30
= 29/30

2007-11-14 12:36:39 · answer #2 · answered by Anonymous · 0 0

a) r things can be chosen from n things in nCr ways. nCr = n! / r! (n-r)!
You have to be familiar with this to solve this problem.
Choose 2 craftsmen out of 5 in 5C2 ways.
Choose 4 laborers out of 6 in 6C4 ways.
In total, (5C2)(6C4) ways.
5! = 5 x 4 x 3 x 2 x 1
5C2=5 x 4 / 2 x 1=10
6C4=6 x 5 / 2 x 1 =15
(10)(15)=150
b)Having cosen the 2 brothers, you have to choose 1 craftsman out of 4 and 3 laborers out of 5.
This can be done in (4C1)(5C3) ways out of the 150 ways.
4C1=4
5C3=10
40/150=0.2667
c)Ignore both brothers.
You have to choose 2 out of 4 craftsmen and 4 out of 5 laborers.
(4C2)(5C4)=6(5)=30
30/150=0.2

2007-11-14 12:50:07 · answer #3 · answered by cidyah 7 · 0 0

wat i dnt get is u have put the answers in the question. so there is no point in answering

2007-11-14 12:29:29 · answer #4 · answered by the pants kind of king 1 · 0 1

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