Question

How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if
(i) 4 letters are used at a time?
(ii) all letters are used at a time?
(iii) all letters are used but first is vowel?

Answer 1

(i) MONDAY has 6 letters with no repetitions, so
Number of words using 4 letters at a time with no repetitions = $6_{P_4}\frac{6!}{2!}=360$
(ii) Number of words using all 6 letters at a time with no repetitions = $6_{P_6}$
$\frac{6!}{(6—6)!}$
=$6\times 5\times 4\times 3\times 2\times 1=720$
(iii) Number of words using all 6 letters, starting with vowels = $2.5_{p_5}=2\times 5\times 4\times 3\times 2\times 1=240$