Problem Solving (PS) | Re: A new word is to be formed by randomly rearranging the letters of the

Total number of ways of arranging the word ALGEBRA is\(\frac{7!}{2!}\)

Now the consonants occupy the same position as in the word ALGEBRA. So consonants will be _LG_BR_.

The 3 vowels in the 3 blanks can be arranged in\(\frac{3!}{2!}\) ways.

The consonants can be arranged in those positions in 4! ways.

As it was said that a new word should be formed, we have to ignore the word ALGEBRA from the list.

\(\frac{3!}{2!} - 1\) number of words.

Probability =\( \frac{(\frac{3!}{2!} - 1) *4!}{\frac{7!}{2!} } \)
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