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# how many different words can be formed with the letters of the word haryana

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## a) How many different words can be formed using the letters of the word HARYANA?b) How many of these begin with H and end with N?c) In how many of these H and N are together?

Click here👆to get an answer to your question ✍️ a) How many different words can be formed using the letters of the word HARYANA?b) How many of these begin with H and end with N?c) In how many of these H and N are together? a) How many different words can be formed using the letters of the word HARYANA?

Question

b) How many of these begin with H and end with N?

c) In how many of these H and N are together?

HARAYANA

Medium Open in App Solution Verified by Toppr

(1)   No. of words that can be formed=

3! 7! ​ = 3! 7×6×5×4×3! ​ =840 words (2)  H_____N No. of such words= 3! 5! ​ = 3! 5×4×3! ​ =20 words

(3)   H andN together  be taken as one letter and can be arranged among themselves in 2! also A is repeated 3 times.

No. of such wordss= 3! 2!×6! ​ = 3! 2×6×5×4×3! ​ =240 words

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## (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 HN as a single letter. Now, HN + ARYAA will give us 6 letters out of which there are 3 A's, 1 R, 1 Y and 1 HN. Total number of all such arrangements =(6!)/(3!)=120. But, H and N can be arranged amongst themselves in 2! ways. Hence, The number of words having H and N together =(120xx2)=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 AAA as 1 letter. Now, we have to arrange 5 letters HRYN + AAA at 5 places. Hence, total number of words formed having all vowels together =5! =(5xx4xx3xx2xx1)=120. Home > English > Class 11 > Maths > Chapter > Permutations >

(i) How many words can be form...

(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?

Updated On: 27-06-2022

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Text Solution Open Answer in App Solution

(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. =7!3!=840.

(ii) Let us consider HN as a single letter.

Now, HN + ARYAA will give us 6 letters out of which there are 3 A's, 1 R, 1 Y and 1 HN.

Total number of all such arrangements

= 6! 3! =120. =6!3!=120.

But, H and N can be arranged amongst themselves in 2! ways.

Hence, The number of words having H and N together

=(120×2)=240. =(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. N=5!3!=20.

(iv) The given word contains 3 vowels AAA and let us treat AAA as 1 letter.

Now, we have to arrange 5 letters HRYN + AAA at 5 places.

Hence, total number of words formed having all vowels together

=5!=(5×4×3×2×1)=120.

=5!=(5×4×3×2×1)=120.

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how many of these begin with H and end with N? स्रोत : www.doubtnut.com

## i How many words can be formed with the letters of the word, 'HARYANA'? How many of theseii 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 theseii have H and N together?iii begin with H and end with N ?iv have 3 vowels together? Home

i How many words can be formed with the letters of the word, 'HARYANA'? How many of theseii have H and N together?iii begin with H and end with N ?iv have 3 vowels together?

Question

(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?

Open in App Solution

(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. Suggest Corrections 2 SIMILAR QUESTIONS

Q.

How many permutations can be formed by the letters of the word, 'VOWELS', when

(i) there is no restriction on letters?

(ii) each word begins with E?

(iii) each word begins with O and ends with L?

(iv) all vowels come together?

(v) all consonants come together?

Q.

How many different words can be formed with the letters of word 'SUNDAY'? How many of the words begin with N. How many begin with N and end in Y ?

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Mohammed 1 month ago

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