DSSSB TGT/PGT/PRT Exam > DSSSB TGT/PGT/PRT Questions > The number of ways so that the birthdays of 6...
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The number of ways so that the birthdays of 6 people falls in exactly 3 calendar months is
- a)118800
- b)36960
- c)158400
- d)47520
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The number of ways so that the birthdays of 6 people falls in exactly ...
No. of ways to choose the 3 months = 12C3 = 220
Now, we have 6 people and 3 months for the birthdays to fall in.
Since none of these three months can have no birthday in it, the 3 possible ways of distributing the 6 people in 3 months would be (4, 1, 1), (3, 2, 1), (2, 2, 2)
(4, 1, 1)
No. of ways of rotating the distribution of the number of birthdays in these three months = 3!/2!
No. of ways of rotating the distribution of the people = 6C4 . 2C1 . 1C1
Therefore, the total number of ways in (4, 1, 1) case
= (3!/21).6C4 . 2C1 . 1C1 = 90 ways
(3, 2, 1)
No. of ways of rotating the distribution of the number of birthdays in these three months = 3!
No. of ways of rotating the distribution of the people = 6C4 . 2C1 . 1C1
Therefore, the total number of ways in (3, 2, 1) case
3!.6C4 . 2C1 . 1C1 = 360 ways
(2, 2, 2)
No. of ways of rotating the distribution of the number of birthdays in these three months
= 3!/3!
No. of ways of rotating the distribution of the people = 6C4 . 2C1 . 1C1
Therefore, total number of ways in (2, 2, 2) case =(3!/3!).6C4 . 2C1 . 1C1 = 90
The number of ways so that the birthdays of 6 people falls in exactly 3 calendar months = (90 + 360 + 90) • 220 = 118800
Now, we have 6 people and 3 months for the birthdays to fall in.
Since none of these three months can have no birthday in it, the 3 possible ways of distributing the 6 people in 3 months would be (4, 1, 1), (3, 2, 1), (2, 2, 2)
(4, 1, 1)
No. of ways of rotating the distribution of the number of birthdays in these three months = 3!/2!
No. of ways of rotating the distribution of the people = 6C4 . 2C1 . 1C1
Therefore, the total number of ways in (4, 1, 1) case
= (3!/21).6C4 . 2C1 . 1C1 = 90 ways
(3, 2, 1)
No. of ways of rotating the distribution of the number of birthdays in these three months = 3!
No. of ways of rotating the distribution of the people = 6C4 . 2C1 . 1C1
Therefore, the total number of ways in (3, 2, 1) case
3!.6C4 . 2C1 . 1C1 = 360 ways
(2, 2, 2)
No. of ways of rotating the distribution of the number of birthdays in these three months
= 3!/3!
No. of ways of rotating the distribution of the people = 6C4 . 2C1 . 1C1
Therefore, total number of ways in (2, 2, 2) case =(3!/3!).6C4 . 2C1 . 1C1 = 90
The number of ways so that the birthdays of 6 people falls in exactly 3 calendar months = (90 + 360 + 90) • 220 = 118800
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The number of ways so that the birthdays of 6 people falls in exactly 3 calendar months isa)118800b)36960c)158400d)47520Correct answer is option 'A'. Can you explain this answer?
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The number of ways so that the birthdays of 6 people falls in exactly 3 calendar months isa)118800b)36960c)158400d)47520Correct answer is option 'A'. Can you explain this answer? for DSSSB TGT/PGT/PRT 2025 is part of DSSSB TGT/PGT/PRT preparation. The Question and answers have been prepared according to the DSSSB TGT/PGT/PRT exam syllabus. Information about The number of ways so that the birthdays of 6 people falls in exactly 3 calendar months isa)118800b)36960c)158400d)47520Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for DSSSB TGT/PGT/PRT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of ways so that the birthdays of 6 people falls in exactly 3 calendar months isa)118800b)36960c)158400d)47520Correct answer is option 'A'. Can you explain this answer?.
The number of ways so that the birthdays of 6 people falls in exactly 3 calendar months isa)118800b)36960c)158400d)47520Correct answer is option 'A'. Can you explain this answer? for DSSSB TGT/PGT/PRT 2025 is part of DSSSB TGT/PGT/PRT preparation. The Question and answers have been prepared according to the DSSSB TGT/PGT/PRT exam syllabus. Information about The number of ways so that the birthdays of 6 people falls in exactly 3 calendar months isa)118800b)36960c)158400d)47520Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for DSSSB TGT/PGT/PRT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of ways so that the birthdays of 6 people falls in exactly 3 calendar months isa)118800b)36960c)158400d)47520Correct answer is option 'A'. Can you explain this answer?.
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