The word MONDAY has 6 distinct letters.
(i) 4 letters out of 6 can be arranged in 6P4 ways.
∴ The required number of words = 6P4 = 6 × 5 × 4 × 3 = 360
(ii) 6 letters can be arranged among themselves in 6P6 ways.
∴ The required number of words = 6P6 = 6!
= 1 × 2 × 3 × 4 × 5 × 6 = 720.
(iii) The first place can be filled by anyone Of the two vowels O or A in 2 ways. The remaining 5 letters can be arranged in the remaining 5 places II to VI in 5P5 = 5! ways.
∴ By the multiplication rule, the required number of words = 2 × 5! = 2 × 1 × 2 × 3 × 4 × 5 = 240