Permutations, with the word STATISTICS?

Four letters are chosen at random from the letters S T A T I S T I C S :





what is the probability exactly two are vowels?





at least two are vowels?





i know that the total number of arrangments is equal to 10!/3!*3!*2! which is equal to 50400. However come someone please help me with these two qurstions. thank you very much

Permutations, with the word STATISTICS?
Well this is a binomial model. Either the one drawn is or isn't a vowel.





There are 10 letters there, 3 of which are vowels. p = 0.30





P(X = 2) = 4 nCr 2 (.3^2)(.7^2)





Then P(X at least 2) = 1 - P(X=1) - P(X=0)





P(X = 1) = 4 nCr 1 (.3)(.7^3)


P(X = 0) = 4 nCr 0 (..3^0)(.7^4)
Reply:since there are 3 vowels





(3c2)*(7c2) / (10c4) is the probability of getting exactly two vowels.





(3c2)*(8c2) / (10c4) is the probability of getting atleast two vowels because out of the 3 vowels you have to choose two and then out of the 8 remaining letters, including the last vowel, you choose two more.





These are set up in the (nCk) format which is n!/[k!(n-k)!]

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