Question

How many words can be formed with tauqeer so that e never comes together?

Answer 1

In the given word tauqeer, there are 7 alphabets out of which 'e' comes twice and rest comes once.

Hence, total number of possible arrangements is given by

[tex]\frac{7!}{2!} \\ \\ =2520[/tex]

Now, let us consider two 'e' as a single unit. Thus, we have the word tauqr(ee). It has 6 letters.

The total number of ways in which 'e' comes together is given by

$6!=720$

Therefore, the number of ways in which e never comes together is

[tex]\text{Total number of arrangements }- \text{Number of ways in which e comes together}  =2520-720\\ =1800[/tex]

Therefore, 1800 words can be formed in which e never comes together.