Discussion

If Suraj does not want the vowels together, then in how many ways can he arrange the letters of the word 'MARKER'?

Answer: C

MARKER has six letters with R twice, and its vowels are A and E.

\[ \text{total arrangements} = \frac{6!}{2!} = 360 \]

Treating the two vowels as one block gives five units:

\[ \frac{5!}{2!} \times 2! = 60 \times 2 = 120 \text{ with the vowels together} \]

\[ 360 - 120 = 240 \]

The division by \( 2! \) throughout accounts for the identical R's.

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