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The number of arrangements of the letters of the word FORTUNE such that the order of vowels is unaltered is x the order of consonants is unaltered is y the order of vowels and consonants is unaltered is Z then x+y/Z=???Pl reply as soon a possible

The number of arrangements of the letters of the word FORTUNE such that the order of vowels is unaltered is x the order of consonants is unaltered is y the order of vowels and consonants is unaltered is Z then x+y/Z=???Pl reply as soon a possible

Grade:12

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
8 years ago
x = ^7C_3 \times 4!, as we select 3 vowels and they are not permuted (retain the order)
similarly
y = ^7C_4 \times 3!

and Z is just selecting places for vowels or consonants =^7C_4

Now solve

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