Question

There are 21 consonants and 5 vowels in English. We wish to make a 4 letter combination as a password for an email account with 3 consonants and 1 vowel (assume all letters are lowercase, and no letter is repeated) How many different passwords can you make?

Answer 1

In a 4 letter word,

Number of ways of selecting (3 consonants out of 21 consonants ) and (1 vowel out of 5 vowels) is

$\binom{21}{3}$$\binom{5}{1}$

=1330*5 = 6650 ways

Now each word contains total 4 letter .

Number of ways the letters arrange among themselves is 4! =24

So, number of password can be made is 6650*24= 159600 ways