How many words with or without meaning can be formed using all the letters of the word ‘MONDAY’ assuming, that no letter is repeated, if all letters are used at a time. $rightwards double arrow$

Solution

Number of letters in word 'Monday' = 6 (all distinct)
Number of vowels = 2 (O and A)
All six letters to be used.
$rightwards double arrow$ n = 6, r = 6
$rightwards double arrow$ Number of permutations = $straight P presuperscript straight n subscript straight r space equals space straight P presuperscript 6 subscript 6 space equals space fraction numerator 6 factorial over denominator 0 factorial end fraction space equals space fraction numerator 6 space straight x space 5 space straight x space 4 space straight x space 3 space straight x space 2 space straight x space 1 space over denominator 1 end fraction space equals 720.$
Hence, the total number of words formed = 720.

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Permutations And Combinations

How many words with or without meaning can be formed using all the letters of the word ‘MONDAY’ assuming, that no letter is repeated, if all letters are used at a time. $rightwards double arrow$

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Determine K, so that K + 2, 4K – 6 and 3K – 2 are three consecutive terms of an A.P.

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