How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY,
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.

Solution:

(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.

$\Rightarrow 2 \times 5 !=240$