The letters of the word “ ZENITH” are written in all possible orde

1.	The letters of the word “ ZENITH” are written in all possible ordered . How many words are possible ifall these words written out as in a dictionary? What is the rank of word “ZENITH”
Answer» In a dictionary the words at each stage are arranged in alphabetical order. In the given problem we must therefore consider the words beginning with E, H, I, N , T, Z in order. ∴ No. of words starting with E=5!=120 No. of words starting with I=5!=120 same as for H, N, T & 3 all are =120 but one of these words if the word ZENITH itself. So, we first find the words begin with ZEH, ZEI & ZENH Now, No. of words starting with ZEH=3!=6 No. of words starting with ZEI=3!=6 No. of words starting with ZENH=2!=2 So we found the first word begining with ZENI is the eord ZENIHT and the next word is ZENITH ∴ Rank of ZENITH =5×120+2×6+2+2 =600+12+4 =616

The letters of the word “ ZENITH” are written in all possible ordered . How many words are possible ifall these words written out as in a dictionary? What is the rank of word “ZENITH”

Answer»

In a dictionary the words at each stage are arranged in alphabetical order. In the given problem we must therefore consider the words beginning with E, H, I, N , T, Z in order.

∴ No. of words starting with E=5!=120

No. of words starting with I=5!=120

same as for H, N, T & 3 all are =120

but one of these words if the word ZENITH itself.

So, we first find the words begin with ZEH, ZEI & ZENH

Now,

No. of words starting with ZEH=3!=6

No. of words starting with ZEI=3!=6

No. of words starting with ZENH=2!=2

So we found the first word begining with ZENI is the eord ZENIHT and the next word is ZENITH

∴ Rank of ZENITH

=5×120+2×6+2+2

=600+12+4

=616

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