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How many strings of eight English letters are there that contain exactly one vowel, if letters can be repeated?

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    What are your thoughts ? – 2017-01-01
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    Please, try to make the titles of your questions more informative. E.g., *Why does $a – 2017-01-01
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    sir i m new here . So take care about thiz in future. – 2017-01-01

2 Answers 2

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Out of 5 vowel 1 vowel.

$\binom{5}{1}$

7 letters can out of 21 consonants can be choosen.

$21^7$

And 1 vowel can be on any 8 places in 8 ways.

Total = $\binom{5}{1} * 21^7 * 8$

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    in other cases we don't need to multiple like u did 8 in thiz ...i know it is stupid question ..but cn u clear it more. – 2017-01-01
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    Suppose you have 5 places __, __, __, __, __ and you have one thing where you can place it? You simply say I have 5 options or ways. So similarly in your case its 8. – 2017-01-01
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    cn u explain thiz question :->How many bit strings of length n contain exactly r 1s? – 2017-01-01
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    Ok I try send me link. – 2017-01-01
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The answer is $21^7\times8\times\binom{5}{1}$. This is because we can choose one vowel in $\binom{5}{1}$ ways. The other $7$ can be filled with $21$ letters(consonants) with repitition. The $8$ accounts for the permutations of the vowels and consonants.