Find the number of ways of arranging the letters of the word MONDAY so

1.	Find the number of ways of arranging the letters of the word MONDAY so that no vowel occupies even place.
Answer» In the word MONDAY there are two vowels, 4 consonants and three even places, three odd places. Since no vowel occupies even place, the two vowels can be filled in the three odd places in ³P₂ ways. The 4 consonants can be filled in the remaining 4 places in 4! ways. ∴ The number of required arrangements = ³P₂ × 4! = 6 × 24 = 144

Find the number of ways of arranging the letters of the word MONDAY so that no vowel occupies even place.

Answer»

In the word MONDAY there are two vowels, 4 consonants and three even places, three odd places.

Since no vowel occupies even place, the two vowels can be filled in the three odd places in ³P₂ ways. The 4 consonants can be filled in the remaining 4 places in 4! ways.

∴ The number of required arrangements

= ³P₂ × 4! = 6 × 24 = 144

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Find the number of ways of arranging the letters of the word MONDAY so that no vowel occupies even place.

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