Answer
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Hint: To solve the above question, we have to use the concept of permutation. We have to find the rank of ‘debac’. We can see that number of words beginning with $a=$ number of arrangements of $b,c,d,e=4!$, And similarly, we can see that number of words beginning with $b,c$ are $4!$ each. In this way, we have to
Solve this problem.
Complete step-by-step solution:
We know that in a dictionary, the words are listed and ranked in alphabetical order. So, in the given we problem have to find the rank of the word $'debac'$.
Now for finding the number of words we have starting with $a$, we have to find the number of arrangements of the remaining 4 letters.
Now, the number of such arrangements is =$4!$
Now we are finding the number of words starting with $b$, we have to find the number of arrangements of the remaining $4$ letters.
Now, the number of such arrangements is =$4!$
Now we are finding the number of words starting with $c$, we have to find the number of arrangements of the remaining $4$ letters.
Now, the number of such arrangements is =$4!$
Now we are finding the number of words starting with $d$ and we are fixing the next letter as $a$, we have to find the number of arrangements of the remaining $3$ letters.
Now, the number of such arrangements is =$3!$
Now we are finding the number of words starting with $d$ and we are fixing the next letter as $b$, we have to find the number of arrangements of the remaining $3$ letters.
Now, the number of such arrangements is =$3!$
Now we are finding the number of words starting with $d$ and we are fixing the next letter as $c$, we have to find the number of arrangements of the remaining $3$ letters.
Now, the number of such arrangements is =$3!$
Now we are finding the number of words starting with $d$, fixing the next letter as e:
Where the first word -$deabc$
And the second word-$deacb$
And the third word-$debac$
So, we can see that number of words which we reach the word $debac=4!+4!+4!+3!+3!+3!+1+1+1=93$
Hence, the correct option is (d) $93$.
Note: Here students must take care of the concept of permutation. Sometimes, the student did a mistake between permutation and combination because they are different. We have to know the main difference between Permutation and combination is ordering. So, students have to take care of it.
Solve this problem.
Complete step-by-step solution:
We know that in a dictionary, the words are listed and ranked in alphabetical order. So, in the given we problem have to find the rank of the word $'debac'$.
Now for finding the number of words we have starting with $a$, we have to find the number of arrangements of the remaining 4 letters.
Now, the number of such arrangements is =$4!$
Now we are finding the number of words starting with $b$, we have to find the number of arrangements of the remaining $4$ letters.
Now, the number of such arrangements is =$4!$
Now we are finding the number of words starting with $c$, we have to find the number of arrangements of the remaining $4$ letters.
Now, the number of such arrangements is =$4!$
Now we are finding the number of words starting with $d$ and we are fixing the next letter as $a$, we have to find the number of arrangements of the remaining $3$ letters.
Now, the number of such arrangements is =$3!$
Now we are finding the number of words starting with $d$ and we are fixing the next letter as $b$, we have to find the number of arrangements of the remaining $3$ letters.
Now, the number of such arrangements is =$3!$
Now we are finding the number of words starting with $d$ and we are fixing the next letter as $c$, we have to find the number of arrangements of the remaining $3$ letters.
Now, the number of such arrangements is =$3!$
Now we are finding the number of words starting with $d$, fixing the next letter as e:
Where the first word -$deabc$
And the second word-$deacb$
And the third word-$debac$
So, we can see that number of words which we reach the word $debac=4!+4!+4!+3!+3!+3!+1+1+1=93$
Hence, the correct option is (d) $93$.
Note: Here students must take care of the concept of permutation. Sometimes, the student did a mistake between permutation and combination because they are different. We have to know the main difference between Permutation and combination is ordering. So, students have to take care of it.
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