25.
The number of words that can be formed using any number of letters of the word
*KANPUR" is
1) 720
2) 1956
3) 360
4) 370
Answers
Step-by-step explanation:
(a)1 Letter word:
Selecting 1 letter of 6 letter K,A,N,P,U,R= ⁶c1
=6 ways
(b)2 Letter words:
Selecting 2 letter of 6 letter K,A,N,P,U,R=
⁶c2
Therefore no. of ways to create 2 letter words =
⁶c2 ×2!
(c)3 Letter words:
Selecting 3 letter of 6 letter K,A,N,P,U,R= ⁶c3
Therefore no. of ways to create 3 letter words =
⁶c3×3!
(d)4 Letter words:
Selecting 4 letter of 6 letter K,A,N,P,U,R= ⁶c4
Therefore no. of ways to create 4 letter words =
⁶c4×4!
(e)5 Letter words:
Selecting 5 letter of 6 letter K,A,N,P,U,R= ⁶c5
Therefore no. of ways to create 5 letter words =
⁶c5×5!
(f)6 Letter words:
Selecting 6 letter of 6 letter K,A,N,P,U,R= ⁶c6
Therefore no. of ways to create 6 letter words =
⁶c6 ×6!
Total =6+ ⁶c2 ×2!+ ⁶c3 ×3!+ ⁶c4 ×4!+ ⁶c5
×5!+6!=1956 words
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The number of words that can be formed using any number of letters of the word "KANPUR" is 1956.
Given:
The word "KANPUR".
To Find:
The number of words that can be formed using any number of letters of the word "KANPUR".
Solution:
- Number of ways in which 1 letter word can be formed:
Selecting 1 letter of 6 letter K,A,N,P,U,R= ⁶c1 =6 ways
- Number of ways in which 2 letter words can be formed.
Selecting 2 letter of 6 letter K,A,N,P,U,R= ⁶c2
Therefore no. of ways to create 2 letter words =⁶c2 ×2!
- Number of ways in which 3 letter words can be formed:
Selecting 3 letter of 6 letter K,A,N,P,U,R= ⁶c3
Therefore no. of ways to create 3 letter words =⁶c3×3!
- Number of ways in which 4 letter words can be formed:
Selecting 4 letter of 6 letter K,A,N,P,U,R= ⁶c4
Therefore no. of ways to create 4 letter words =⁶c4×4!
- Number of ways in which 5 letter words can be formed:
Selecting 5 letter of 6 letter K,A,N,P,U,R= ⁶c5
Therefore no. of ways to create 5 letter words =⁶c5×5!
- Number of ways in which 6 letter words can be formed:
Selecting 6 letter of 6 letter K,A,N,P,U,R= ⁶c6
Therefore no. of ways to create 6 letter words =⁶c6 ×6!
Total no. of ways =6+ ⁶c2 ×2!+ ⁶c3 ×3!+ ⁶c4 ×4!+⁶c5×5!+ ⁶c6 ×6!=1956 words.
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