Exercise-2.2

1.  (iii) Find the  number of 5 letter words that can be formed using the letters of the word ' NATURE ' that begin with N when repetition is allowed

(v)Find the number of functions from set A containing 5 elements  into a set B containing 4 elements

 

5 letter word that can be formed using the letters of the word NATURE begin with N repetition is allowed
consider 5 places 

Fill the first place using N in 1 way Each of the remaining 4 places can be filled using N,A,T,U,R,E in 6 ways 
No. of words =$1\times 6\times 6\times 6\times 6$
                       $=6^4=1296.$
No.of elements in A =n(A)=5
No.of elements in A = n(B) = 4
Total number of functions from A to B =$n(B{)}^{n\left(A\right)}=4^5$