M L Aggarwal Solutions for Chapter: Permutations and Combinations, Exercise 4: EXERCISE 8.4

Find the number of arrangements that can be made out of the following word:

$\mathrm{CIVILIZATION}$

How many numbers greater than $100000$ can be formed by using the digits $2, 4, 2, 3, 0, 2$ taken all together?

How many arrangements can be made with the letters of the word $\mathrm{MATHEMATICS}$ if there is no restriction?

How many arrangements can be made with the letters of the word $\mathrm{MATHEMATICS}$ if vowels occur together?

How many arrangements can be made with the letters of the word $\mathrm{MATHEMATICS}$ if all vowels don't occur together ?

How many arrangements can be made with the letters of the word $\mathrm{MATHEMATICS}$ if consonants occur together ?

How many arrangements can be made with the letters of the word $\mathrm{MATHEMATICS}$ if $M$ is at both extremes?

How many arrangements can be made with the letters of the word $\mathrm{MATHEMATICS}$ if order of vowels remains unchanged?