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Question

How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?

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Solution

In MORADABAD total letters = 9. In which there are 3A's , 2D'sand 4different letters.Case-1:No. of words formed from 4 different letters,C46×4!=15×24=360Case-2:No. of words formed from 2 alike and 2 different letters,=C12×C25×4!2!=2×10×12=240Case-3:No. of words formed from 3 alike and 1 different letters,=1×C15×4!3!=5×4=20Case-4:No. of words formed from 2 alike of one kind and 2 alike of other kind,=C22×4!2!×2!=1×6=6So number of required words= 360+240+20+6=626

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