Question 197539: a) Using the letters in the word "OCTAGON," how many distinct arrangements using all 7 letters are possible?
b) Using the letters in the word "TRAPEZOID," how many distinct combinations using 7 letters at a time are possible?
c) Using the letters in the word "SQUARE," what is the probability that a 6-letter arrangement the first 2 letters are vowels?
d) Using the letters in the word "RHOMBUS," what is probability that in a 7-letter arrangement the first 3 letters are vowels?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! a) Using the letters in the word "OCTAGON," how many distinct arrangements using all 7 letters are possible?
Ans: 7!/2! = 2520
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b) Using the letters in the word "TRAPEZOID," how many distinct combinations using 7 letters at a time are possible?
Ans: 9P7 = 9!/(9-7)! = 9!/2! = 181440
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c) Using the letters in the word "SQUARE," what is the probability that a 6-letter arrangement the first 2 letters are vowels?
# of ways to pick the two vowels: 3C2 = 3
# of ways to arrange those two vowels = 2
# of ways to arrange the rest of the letters = 4! = 24
# of ways to arrange the 6 letters with no special restrictions: 6!
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Ans: Probability of satisfying the condition = [3*2*24]/6! = 0.2
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d) Using the letters in the word "RHOMBUS," what is probability that in a 7-letter arrangement the first 3 letters are vowels?
Pick three vowels: 0 ways because there are not three vowels in RHOMBUS.
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Cheers,
Stan H.
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