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if the letters of the ward FATHER are permuted in all the possible ways and the words thus formed are arranged in dictionary order find the rank of the word FATHER
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if the letters of the ward FATHER are permuted in all the possible way...
Rank of the Word FATHER
To find the rank of the word FATHER, we need to first find all the words that can be formed by permuting its letters.
Permutations of the Letters in FATHER
The word FATHER has 6 letters. Therefore, the total number of permutations possible is:
n! = 6! = 720
Let us list all the words that can be formed by permuting the letters in FATHER:
- AEFHRT
- AEFHTR
- AEFTHR
- AEFTRH
- AEFRTH
- AEFRTF
- AERFTH
- AERFHT
- AERTFH
- AERTHF
- AERTFH
- AERTHF
- AFEHRT
- AFEHTR
- AFETHR
- AFETRH
- AFERTH
- AFERTF
- AFRETH
- AFREHT
- AFRTHE
- AFRTEH
- AFRETH
- AFRETH
- AFRTEH
- AFRTHE
- ATFHER
- ATFHER
- ATFEHR
- ATFERH
- ATFRHE
- ATFREH
- ATRFHE
- ATRFEH
- ATREFH
- ATREHF
- ATREHF
- ATREFH
- AHFERF
- AHFERT
- AHFTRE
- AHFTER
- AHFETR
- AHFERT
- AHRFET
- AHRFTE
- AHREFT
- AHRETF
- AHRTEF
- AHRTFE
- AHTFER
- AHTFRE
- AHTEFR
- AHTERF
- AHTRFE
- AHTREF
- ARFEHT
- ARFETH
- ARFTEH
- ARFTHE
- ARFETH
- ARFEHT
- ARHETF
- ARHTEF
- ARHEFT
- ARHETF
- ARHTFE
- ARHTEF
- ARTEFH
- ARTEHF
- ARTFEH
- ARTFHE
Community Answer
if the letters of the ward FATHER are permuted in all the possible way...
Number of words starting with A =5!=120
Number of words starting with E =5!=120
Number of words starting with FAE =3!=6
Number of words starting with FAH=3!=6
Number of words starting with FAR =3!=6
Number of words starting with FATE =2!=2
Next word is 'FATHER'
Therefore rank
=120+120+6+6+6+2+1= 261
Number of words starting with E =5!=120
Number of words starting with FAE =3!=6
Number of words starting with FAH=3!=6
Number of words starting with FAR =3!=6
Number of words starting with FATE =2!=2
Next word is 'FATHER'
Therefore rank
=120+120+6+6+6+2+1= 261
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if the letters of the ward FATHER are permuted in all the possible ways and the words thus formed are arranged in dictionary order find the rank of the word FATHER Related: Permutations and Combinations, Chapter Notes, Class 11, Maths
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