Question

Letters of the word 'MOTHER' are arranged at random. Find the number of arrangement of :

i) vowels are together. ii) vowels are never together

iii) Begin with o and end with I.​

Answer 1

Answer:

Total letter = 6 (M,O,T,H,E,R)

consonants = 4 (M,T,H,R)

vowels = 2 (O,E)

✿ total arrangement = 6! = 720

✿ vowels together = 2! × 5! = 240

✿ vowels not together = 720-240 = 480

( or ) 5p2 × 4! = 20×24 = 480

✿ begin with 0 and end with l so two places is fix only 3 place arrang = 3! = 6

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