Number of different words that can be formed using all the letters of the word "DEEPMALA" if two vowels of same kind are together and the other two are also together but separated from the first two is

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Number of different words that can be formed using all the

letters of the word "DEEPMALA" if two vowels of same

kind are together and the other two are also together but

separated from the first two is

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1440

960

1200

2160

answer is D.

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Detailed Solution

| D | P | M | L | can be arranged in 4! ways & the two gaps

out of 5 gaps can be selected in $^{5} C_{2}$ ways.

two A's and two E's can be atranged in $\frac{4!}{2! 2!} = 6$ ways.

$∴$ Total number of arrangements $= 4! \cdot^{5} C_{2} \cdot \frac{4!}{2! 2!}$

$= 1440$

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