(i) How many words can be formed with the letters of the word, 'HARYANA'? How many of these
(ii) have H and N together ?
(iii) begin with H and end with N ?
(iv) have 3 vowels together?
(i) How many words can be formed with the letters of the word, 'HARYANA'? How many of these
(ii) have H and N together ?
(iii) begin with H and end with N ?
(iv) have 3 vowels together?
(i) The given word ' HARYANA' consists of 7 letters, out of which there are 1 H, 3 A's, 1 R, 1 Y and 1 N.
Total number of words formed by all the letters of the given word = 7 !3 !=840.
(ii) Let us consider 
as a single letter.
Now, 
+ ARYAA will give us 6 letters out of which there are 3 A' s, 1 R, 1 Y and 1 
.
Total number of all such arrangments = 6 !3 !=120.
But, H and N can be arranged amost themselves in 2 ! ways.
Hence, the number of words having H and N together = (120×2)=240.
(iii) After fixing H in first place and N in last place, we have 5 letters, out of which there are 3 A' s, 1 R and 1 Y.
Hence, the number of words beginning with H and ending with N=5 !3 !=20.
(iv) The given word contains 3 vowels AAA and let us treat 
as 1 letter.
Now, we have to arrange 5 letters HRYN+ 
at 5 places.
Hence, total number of words formed having all vowels together = 5 !=(5×4×3×2×1)=120.
(i) The given word ' HARYANA' consists of 7 letters, out of which there are 1 H, 3 A's, 1 R, 1 Y and 1 N.
Total number of words formed by all the letters of the given word = 7 !3 !=840.
(ii) Let us consider as a single letter.
Now, + ARYAA will give us 6 letters out of which there are 3 A' s, 1 R, 1 Y and 1 .
Total number of all such arrangments = 6 !3 !=120.
But, H and N can be arranged amost themselves in 2 ! ways.
Hence, the number of words having H and N together = (120×2)=240.
(iii) After fixing H in first place and N in last place, we have 5 letters, out of which there are 3 A' s, 1 R and 1 Y.
Hence, the number of words beginning with H and ending with N=5 !3 !=20.
(iv) The given word contains 3 vowels AAA and let us treat as 1 letter.
Now, we have to arrange 5 letters HRYN+ at 5 places.
Hence, total number of words formed having all vowels together = 5 !=(5×4×3×2×1)=120.
