How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY,
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.
(i) The word MONDAY consists of 6 letters.
Number of words formed using 4 letters = Number of arrangements of 6 letters, taken 4 at a time $={ }^{6} P_{4}=\frac{6 !}{2 !}=6 \times 5 \times 4 \times 3=360$
(ii) Number of words formed using all the letters = Number of arrangements of 6 letters, taken all at a time = 6P6 = 6! = 720
(iii) The word MONDAY consists of 2 vowels and 4 consonants.
The first letter has to be a vowel, which is to be chosen from the two vowels.
This can be done in two ways. The remaining 5 letters can be arranged in 5! ways to form 6 letter words.
$\Rightarrow 2 \times 5 !=240$