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The number of ways in which 12 students can be equally divided into three groups is (a) 5775 (b) 7575 (c) 7755 (d) none of these?
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The number of ways in which 12 students can be equally divided into th...
Solution:
Dividing 12 students into three groups means that each group will have 4 students because 4 × 3 = 12.
We can find the number of ways to divide 12 students into three groups by using the formula for combinations, which is:
nCr = n! / r! (n – r)!
where n is the total number of items, and r is the number of items we want to choose.
In this case, n = 12 and r = 4, because we want to choose 4 students for each group.
So the number of ways to divide 12 students into three groups is:
12C4 × 8C4
= (12! / 4! 8!) × (8! / 4! 4!)
= (12 × 11 × 10 × 9 / 4 × 3 × 2 × 1) × (8 × 7 × 6 × 5 / 4 × 3 × 2 × 1)
= 495 × 70
= 34650
Therefore, the correct answer is (d) none of these, as none of the given options match the calculated value of 34650.
Dividing 12 students into three groups means that each group will have 4 students because 4 × 3 = 12.
We can find the number of ways to divide 12 students into three groups by using the formula for combinations, which is:
nCr = n! / r! (n – r)!
where n is the total number of items, and r is the number of items we want to choose.
In this case, n = 12 and r = 4, because we want to choose 4 students for each group.
So the number of ways to divide 12 students into three groups is:
12C4 × 8C4
= (12! / 4! 8!) × (8! / 4! 4!)
= (12 × 11 × 10 × 9 / 4 × 3 × 2 × 1) × (8 × 7 × 6 × 5 / 4 × 3 × 2 × 1)
= 495 × 70
= 34650
Therefore, the correct answer is (d) none of these, as none of the given options match the calculated value of 34650.
Community Answer
The number of ways in which 12 students can be equally divided into th...
Total 12ways
12*11*10*9*8.....=479001600/4*4*4*3=5775
12*11*10*9*8.....=479001600/4*4*4*3=5775
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The number of ways in which 12 students can be equally divided into three groups is (a) 5775 (b) 7575 (c) 7755 (d) none of these?
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The number of ways in which 12 students can be equally divided into three groups is (a) 5775 (b) 7575 (c) 7755 (d) none of these? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of ways in which 12 students can be equally divided into three groups is (a) 5775 (b) 7575 (c) 7755 (d) none of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of ways in which 12 students can be equally divided into three groups is (a) 5775 (b) 7575 (c) 7755 (d) none of these?.
The number of ways in which 12 students can be equally divided into three groups is (a) 5775 (b) 7575 (c) 7755 (d) none of these? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of ways in which 12 students can be equally divided into three groups is (a) 5775 (b) 7575 (c) 7755 (d) none of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of ways in which 12 students can be equally divided into three groups is (a) 5775 (b) 7575 (c) 7755 (d) none of these?.
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