No. of letters in the word MONDAY = 6 (i) When 4 letters are used at a time. Then, the required number of words = $\,{}^{6}P_{4}$ = $6!/2!$ = 6 × 5 × 4 × 3 = 360 (ii) When all letters are used at a time. Then the required number of words = $\,{}^{6}P_{6}$ = 6! = 720 (iii) All letters are used but first letter is a vowel. So the first letter can be either A or O. So there are 2 ways to fill the first letter & remaining places can be filled in $\,{}^{5}P_{5}$ ways. ∴ The required number of words = 2 × $\,{}^{5}P_{5}$ = 2 × 5! = 240.