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Question-201631




Question Number 201631 by professorleiciano last updated on 09/Dec/23
Answered by mr W last updated on 10/Dec/23
totally number of words: 6!=720    number of words in which 3 vowels  are together: 4!3!=144    number of words in which 3 vowels  are not together: 720−144=576  ⇒probability p=((576)/(720))=80%  i.e. answer (e) is correct.
$${totally}\:{number}\:{of}\:{words}:\:\mathrm{6}!=\mathrm{720} \\ $$$$ \\ $$$${number}\:{of}\:{words}\:{in}\:{which}\:\mathrm{3}\:{vowels} \\ $$$${are}\:{together}:\:\mathrm{4}!\mathrm{3}!=\mathrm{144} \\ $$$$ \\ $$$${number}\:{of}\:{words}\:{in}\:{which}\:\mathrm{3}\:{vowels} \\ $$$${are}\:\boldsymbol{{not}}\:{together}:\:\mathrm{720}−\mathrm{144}=\mathrm{576} \\ $$$$\Rightarrow{probability}\:{p}=\frac{\mathrm{576}}{\mathrm{720}}=\mathrm{80\%} \\ $$$${i}.{e}.\:{answer}\:\left({e}\right)\:{is}\:{correct}. \\ $$

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