A P Prabhakaran Solutions for Chapter: Permutations and Combinations, Exercise 2: SELF EVALUATION TEST

How many words can be formed with or without meaning can be formed using the letters of the word $‘EQUATION\text{'}$, using each letter exactly once?

How many words can be formed using the letters of the word $‘TRIANGLE\text{'}$? 

A student has to answer $7$ questions out of $12$questions which are divided into two, each containing $6$ questions. He is not permitted to attempt more than $5$questions from each group. In how many ways can he choose $7$questions? 

How many different words can be formed using all the letters of the word$‘ALLAHABAD\text{'}$?

How many different words can be formed using all the letters of the word $‘ALLAHABAD\text{'}$$?$ In how many of them vowels occupy odd places$?$

Different words can be formed using all the letters of the word 'ALLAHABAD. In How many of them both L's do not come together?

In how many ways $9$ examinations papers be arranged so that the best and worst papers are never together? 

If ${}^{22}{\mathrm{P}}_{r+1}{:}^{20}{\mathrm{P}}_{r+2}=11:52$, find $r$