**Illustration 1: **

(a) How many anagrams can be made by using the letters of the word HINDUSTAN?

*(b) How many of these anagrams begin and end with a vowel.*

*(c) In how many of these anagrams, all the vowels come together.*

*(d) In how many of these anagrams, none of the vowels come together.*

*(e) In how many of these anagrams, do the vowels and the consonants occupy the same relative positions as in HINDUSTAN?*

*Solution:*

*Illustration **2: *

*How many 3 digit numbers can be formed using the digits 0, 1, 2,3,4,5 so that *

* (a) Digits may not be repeated *

* (b) Digits may be repeated*

**Solution: **

(a) Let the 3-digit number be XYZ

Position (X) can be filled by 1, 2,3,4,5 but not 0. So it can be filled in 5 ways.

Position (Y) can be filled in 5 ways again. (Since 0 can be placed in this postion).

Position (Z) can be filled in 4 ways.

Hence, by the fundamental principle of counting, total number of ways is

5 x 5 x 4 = 100 ways.

(b) Let the 3 digit number be XYZ

Position (X) can be filled in 5 ways

Position (Y) can be filled in 6ways.

Position (Z) can be filled in 6 ways.

Hence by the fundamental principle of counting, total number of ways is

5 x 6 x 6 = 180.

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