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Question 1161906: A committee of three people is selected at random from a set consisting of five teachers, four parents of students, and six alumni. (a) What is the probability of the event that the committee consists of all teachers? (b) What is the probability of the event that the committee consists of all parents? (c) What is the probability of the event that there will be at least 1 teacher on the committee?
Formula for (a) is: nPr = n!/r!(n-r)! note:the second part of (a) the formula being used is nCr= n!/r!(n-r)!
Formula for (b) is: nCr=n!/r!(n-r)!
Formula for (c) is: nCr=n!/r!(n-r)!
Tutor my answer for this is wrong, here is what I did. 5P3 = 5!/3!(5-3)! = 5!/3!(2)! = 5*4*3/3*2*1 = 10. The second part of (a) 16C3 =16!/3!(16-3)! = 16!/3!(13)! = 16*15*14*/3*2*1 =560. The last step 10/560 = 0.171 (Round to three decimal places as needed).
(b) 4C3 = 4!/3!(4-3)! = 4!/3!(1)! = 4*3*2/3*2*1 = 4. Next step I did 4/560 = 0.007.
(c) 10C3 = 10!/3!(10-3)! = 10!/3!(7)! = 10*9*8/3*2*1 = 120. next 120/560 = 0.214 next. 1 - 0.214 = 0.786
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
In your posts, you keep showing the formulas for nPr and nCr being the same; they are not.
nPr is the PERMUTATION of n things r at a time; in a permutation, order matters. The formula for the number of permutations is
nPr = n!/(n-r)!
In a final race with 8 competitors, the number of ways to award first and second places (order matters) is 8P2 = 8!/6! = 8*7 = 56.
nCr is the COMBINATION of n things r at a time; in a combination, order does not matter. The formula for the number of combinations is
nCr = n!/(r!(n-r)!)
In a preliminary race with 8 competitors, the number of ways to select 2 of them to move to the next round (order does not matter) is 8C2 = 8!/(2!(6!)) = (8*7)/(2*1) = 28.
In this problem, there is nothing that involves permutations; you are selecting a committee, so order does not matter. So all the calculations involve nCr.
As for your wrong answer, most if not all of the reason is that there are only 15 people total, not 16. So the denominator of your probability fractions is 15C3, not 16C3.
(a) 5C3/15C3 [all 3 are teachers]
(b) 4C3/15C3 [all 3 are parents]
(c) 1-10C3/15C3 [not 0 are teachers]
Do the calculations again and see if you get the right answers.
Re-post if you still have questions.
By the way... thanks for showing the work you did. VERY few users of this forum do that.
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