SOLUTION: In how many ways can the letters of the word 'PROBABILITY' be arranged if 1)it begins with 'I' 2)it must start with a consonant and end witg a vowel 3)'A' must be exactly in the

Algebra ->  Permutations -> SOLUTION: In how many ways can the letters of the word 'PROBABILITY' be arranged if 1)it begins with 'I' 2)it must start with a consonant and end witg a vowel 3)'A' must be exactly in the      Log On


   



Question 1024646: In how many ways can the letters of the word 'PROBABILITY' be arranged if
1)it begins with 'I'
2)it must start with a consonant and end witg a vowel
3)'A' must be exactly in the middle

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
In how many ways can the letters of the word 'PROBABILITY' be arranged if
1)it begins with 'I'
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2 ways to place the I leaving 10 letters to arrange in 10!/(2!) ways
Ans: 2*10!/2! = 10!
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2)it must start with a consonant and end with a vowel
4 vowels ; 7 consonants
(4/2)(7/2) = 7 ways to place the 1st and last letters
9! ways to arrange the in between set
Ans: 7*9! arrangements
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3)'A' must be exactly in the middle
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I'll leave that to you.
Cheers,
Stan H.
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