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Find the number of 4- letter words that ...

Find the number of 4- letter words that can be formed using the letters of the word. MIRACLE. How many of them
end with a consonant ?

Text Solution

Verified by Experts

The word MIRACLE has 7 letters. The number of 4 letter words that can be formed using these letters `=""^(7)P_(4)=7xx6xx5xx4=840` Now take 4 blanks
`square " " square " " square " " square`
We can fill the last place with one of the 4 consonants `{C, L, R, M}" in "^(4)P_(1)=4` ways. The remaining 3 places can be filled with the remaining 6 letters in `""^(6)P_(3)=6xx5xx4=120` ways.
`therefore` The number of 4 letter words that end with a consonant is `=4xx120=480` ways.
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Knowledge Check

  • The number of 5-letter words that can be formed by using the letters of the word SARANAM is

    A
    1120
    B
    6720
    C
    480
    D
    720

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