SOLUTION: Combinations Question: Find the number of ways in which each committee can be selected. 1. a committe of 5 people from a group of 8 people 2. a committe of 2 people from a gro

Algebra ->  Permutations -> SOLUTION: Combinations Question: Find the number of ways in which each committee can be selected. 1. a committe of 5 people from a group of 8 people 2. a committe of 2 people from a gro      Log On


   

Question 93530: Combinations
Question: Find the number of ways in which each committee can be selected.
1. a committe of 5 people from a group of 8 people
2. a committe of 2 people from a group of 16 people
3. a committe of 4 people from a group of 7people
4. a committe of 8 people from a group of 15people
5. a committe of 3 people from a group of 8 people
Question: At luncheon guest are offered a selection of 4 diffrent grilled vegetables and 5 diffrent relishes. In how many ways can the following items be chosen?
6. 2 vegetables and 3 relishes
7. 3 vegetables and 2 relishes
8. 4 vegetables and 4 relishes
9. 3 vegetables and 3 relishes
Question: A bag contains 8 white marbles and 7 blue marbles. Find the probability of selecting each combination
10. 2 white and 3 blue
11. 3 white and 2 blue
12. 4 white and 1 blue
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do one from each section. The others in that section are worked the same.
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Question: Find the number of ways in which each committee can be selected.
1. a committe of 5 people from a group of 8 people
8C5 = 8C3 = [8*7*6]/[1*2*3] = 56
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Question: At luncheon guest are offered a selection of 4 diffrent grilled vegetables and 5 diffrent relishes. In how many ways can the following items be chosen?
6. 2 vegetables and 3 relishes
# of ways to pick 2 vegetables = 4C2 = [4*3]/[1*2] = 6
# of ways to pick 3 relishes = 5C3 = 5C2 = [5*4]/[1/2]=]10
So, # of ways to pick 2 veg and 3 rel = 6*10 = 60
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Question: A bag contains 8 white marbles and 7 blue marbles. Find the probability of selecting each combination
10. 2 white and 3 blue
# of ways to pick 2 white = 8C2 = 28
# of ways to pick 3 blue = 7C3 = 35
So, # of ways to pick 2 white and 3 blue = 28*35
So 28*35 is the number of ways to succeed
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The number of possible outcomes of selecting 5 marbles from 15 is 15C5= 3003
Therefore the probability of selecting 2 white and 3 blue is [28*35]/3003
= 980/3003 = 0.3263...
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Cheers,
Stan H.