# 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?

HARAYANAMedium 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.

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(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?## 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?

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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

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(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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