Permutations And Combinations

Question
CBSEENMA11014109

How many words, with or without meaning, can be formed with the letters of word ‘MONDAY’ assuming, that no letter is repeated, if 4 letters are used but the first letter is a vowel ?

Solution

Number of letters in word 'MONDAY' = 6 (all district)
    Number of vowels = 2 (O and A)
Number of letters to be used in 4 and first letter is a vowel,
rightwards double arrow   
             
Number of arrangements for box 1 = straight P presuperscript 2 subscript 1 space equals space fraction numerator 2 factorial over denominator 1 factorial end fraction equals 2                                         (i)
(Two vowels for 1 box)
We now have 5 letters left and 3 boxes for them.
rightwards double arrow                            n = 5,  r = 3
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#6 {main}</pre>  ...(ii)
Hence, from (i) and (ii), the total number of permutations i.e., the number of words formed:
                                               = 2 x 60 = 120.

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Some More Questions From Permutations and Combinations Chapter

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