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If permutations of 4 letters taken from the word 'MATHEMATICS' is A and permutations of 4 letters taken from the word 'EXAMINATION' is B then lA-Bl equals (a)0! (b)3! (c)2! (d)none of these?
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If permutations of 4 letters taken from the word 'MATHEMATICS' is A an...
**Solution:**
To find the permutation of 4 letters taken from the word 'MATHEMATICS', we first need to determine the number of ways to select 4 letters from the given word.
The word 'MATHEMATICS' has a total of 11 letters. So, the number of ways to select 4 letters from the word is given by the combination formula:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of items and r is the number of items to be selected.
In this case, n = 11 (total number of letters) and r = 4 (number of letters to be selected).
C(11, 4) = 11! / (4!(11-4)!)
= 11! / (4! * 7!)
= (11 * 10 * 9 * 8) / (4 * 3 * 2 * 1)
= 3,960
So, there are 3,960 permutations of 4 letters taken from the word 'MATHEMATICS'. We can represent this as A = 3,960.
Similarly, to find the permutation of 4 letters taken from the word 'EXAMINATION', we need to determine the number of ways to select 4 letters from the given word.
The word 'EXAMINATION' has a total of 11 letters. So, the number of ways to select 4 letters from the word is given by the combination formula:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of items and r is the number of items to be selected.
In this case, n = 11 (total number of letters) and r = 4 (number of letters to be selected).
C(11, 4) = 11! / (4!(11-4)!)
= 11! / (4! * 7!)
= (11 * 10 * 9 * 8) / (4 * 3 * 2 * 1)
= 3,960
So, there are 3,960 permutations of 4 letters taken from the word 'EXAMINATION'. We can represent this as B = 3,960.
Now, we need to calculate lA - Bl.
lA - Bl = 3,960 - 3,960
= 0
Therefore, the value of lA - Bl is 0.
Hence, the correct option is (a) 0!
To find the permutation of 4 letters taken from the word 'MATHEMATICS', we first need to determine the number of ways to select 4 letters from the given word.
The word 'MATHEMATICS' has a total of 11 letters. So, the number of ways to select 4 letters from the word is given by the combination formula:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of items and r is the number of items to be selected.
In this case, n = 11 (total number of letters) and r = 4 (number of letters to be selected).
C(11, 4) = 11! / (4!(11-4)!)
= 11! / (4! * 7!)
= (11 * 10 * 9 * 8) / (4 * 3 * 2 * 1)
= 3,960
So, there are 3,960 permutations of 4 letters taken from the word 'MATHEMATICS'. We can represent this as A = 3,960.
Similarly, to find the permutation of 4 letters taken from the word 'EXAMINATION', we need to determine the number of ways to select 4 letters from the given word.
The word 'EXAMINATION' has a total of 11 letters. So, the number of ways to select 4 letters from the word is given by the combination formula:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of items and r is the number of items to be selected.
In this case, n = 11 (total number of letters) and r = 4 (number of letters to be selected).
C(11, 4) = 11! / (4!(11-4)!)
= 11! / (4! * 7!)
= (11 * 10 * 9 * 8) / (4 * 3 * 2 * 1)
= 3,960
So, there are 3,960 permutations of 4 letters taken from the word 'EXAMINATION'. We can represent this as B = 3,960.
Now, we need to calculate lA - Bl.
lA - Bl = 3,960 - 3,960
= 0
Therefore, the value of lA - Bl is 0.
Hence, the correct option is (a) 0!
Community Answer
If permutations of 4 letters taken from the word 'MATHEMATICS' is A an...
Permutations of both A and B are same hence lA-Bl is zero and right option is none of these
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If permutations of 4 letters taken from the word 'MATHEMATICS' is A and permutations of 4 letters taken from the word 'EXAMINATION' is B then lA-Bl equals (a)0! (b)3! (c)2! (d)none of these?
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If permutations of 4 letters taken from the word 'MATHEMATICS' is A and permutations of 4 letters taken from the word 'EXAMINATION' is B then lA-Bl equals (a)0! (b)3! (c)2! (d)none of these? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If permutations of 4 letters taken from the word 'MATHEMATICS' is A and permutations of 4 letters taken from the word 'EXAMINATION' is B then lA-Bl equals (a)0! (b)3! (c)2! (d)none of these? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If permutations of 4 letters taken from the word 'MATHEMATICS' is A and permutations of 4 letters taken from the word 'EXAMINATION' is B then lA-Bl equals (a)0! (b)3! (c)2! (d)none of these?.
If permutations of 4 letters taken from the word 'MATHEMATICS' is A and permutations of 4 letters taken from the word 'EXAMINATION' is B then lA-Bl equals (a)0! (b)3! (c)2! (d)none of these? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If permutations of 4 letters taken from the word 'MATHEMATICS' is A and permutations of 4 letters taken from the word 'EXAMINATION' is B then lA-Bl equals (a)0! (b)3! (c)2! (d)none of these? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If permutations of 4 letters taken from the word 'MATHEMATICS' is A and permutations of 4 letters taken from the word 'EXAMINATION' is B then lA-Bl equals (a)0! (b)3! (c)2! (d)none of these?.
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