Question

the no. of words can be formed from the letters of the word 'MAXIMUM', if two consonants cannot occur together , is ??

Answer 1

Dear student

$$\begin{gathered} \mathrm{In}\mathrm{a}\mathrm{word}\mathrm{MAXIMUM},\mathrm{there}\mathrm{are}4\mathrm{consonants}\left(\mathrm{i}.\mathrm{e}.\mathrm{M},\mathrm{A},\mathrm{M},\mathrm{M}\right)\mathrm{and} \\ \mathrm{three}\mathrm{vowels}\left(\mathrm{i}.\mathrm{e}.\mathrm{A},\mathrm{I},\mathrm{U}\right) \\ \mathrm{If}\mathrm{we}\mathrm{fix}\mathrm{the}\mathrm{position}\mathrm{of}\mathrm{vowels}\mathrm{ie}\mathrm{A},\mathrm{I},\mathrm{U}\mathrm{the}\mathrm{pointed}\mathrm{place}\mathrm{to}\mathrm{be}\mathrm{filled} \\ \mathrm{by}\mathrm{M},\mathrm{X},\mathrm{M},\mathrm{M} \\ \mathrm{So},\mathrm{required}\mathrm{number}\mathrm{of}\mathrm{ways}=\frac{3!\times 4!}{3!}=4! \end{gathered}$$
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