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A box contains tickets numbered from 1 to 24. 3 tickets are to be chosen to give 3 prizes. What is the probability that at least 2 tickets contain a number which is multiple of 3?
- a)35/256
- b)33/220
- c)63/253
- d)43/190
- e)59/253
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A box contains tickets numbered from 1 to 24. 3 tickets are to be chos...
From 1 to 24, there are 8 numbers which are multiple of 3
Case 1: 2 are multiple of 3, and one any other number from (24-8) = 16 tickets
8C2 * 16C1 / 24C3 = 56/253
Case 2: all are multiples of 3.
8C3 / 24C3 = 7/253
Add both cases.
Case 1: 2 are multiple of 3, and one any other number from (24-8) = 16 tickets
8C2 * 16C1 / 24C3 = 56/253
Case 2: all are multiples of 3.
8C3 / 24C3 = 7/253
Add both cases.
Most Upvoted Answer
A box contains tickets numbered from 1 to 24. 3 tickets are to be chos...
Solution:
Total number of ways to choose 3 tickets from 24 = 24C3
Number of ways to choose 3 tickets such that none of them is a multiple of 3 = Number of ways to choose 3 tickets from the 16 remaining tickets (not divisible by 3) = 16C3
Number of ways to choose 3 tickets such that exactly 1 ticket is a multiple of 3 = Number of ways to choose 1 ticket from the 8 tickets which are divisible by 3 and 2 tickets from the 16 remaining tickets (not divisible by 3) = 8C1 x 16C2
Number of ways to choose 3 tickets such that at least 2 tickets are multiples of 3 = Total number of ways to choose 3 tickets - (Number of ways to choose 3 tickets such that none of them is a multiple of 3 + Number of ways to choose 3 tickets such that exactly 1 ticket is a multiple of 3)
= 24C3 - 16C3 - 8C1 x 16C2
= 253
Therefore, the probability of choosing 3 tickets such that at least 2 tickets are multiples of 3 = Number of ways to choose 3 tickets such that at least 2 tickets are multiples of 3 / Total number of ways to choose 3 tickets from 24
= 253/24C3
= 63/253
Hence, option (c) is the correct answer.
Total number of ways to choose 3 tickets from 24 = 24C3
Number of ways to choose 3 tickets such that none of them is a multiple of 3 = Number of ways to choose 3 tickets from the 16 remaining tickets (not divisible by 3) = 16C3
Number of ways to choose 3 tickets such that exactly 1 ticket is a multiple of 3 = Number of ways to choose 1 ticket from the 8 tickets which are divisible by 3 and 2 tickets from the 16 remaining tickets (not divisible by 3) = 8C1 x 16C2
Number of ways to choose 3 tickets such that at least 2 tickets are multiples of 3 = Total number of ways to choose 3 tickets - (Number of ways to choose 3 tickets such that none of them is a multiple of 3 + Number of ways to choose 3 tickets such that exactly 1 ticket is a multiple of 3)
= 24C3 - 16C3 - 8C1 x 16C2
= 253
Therefore, the probability of choosing 3 tickets such that at least 2 tickets are multiples of 3 = Number of ways to choose 3 tickets such that at least 2 tickets are multiples of 3 / Total number of ways to choose 3 tickets from 24
= 253/24C3
= 63/253
Hence, option (c) is the correct answer.
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Community Answer
A box contains tickets numbered from 1 to 24. 3 tickets are to be chos...
From 1 to 24, there are 8 numbers which are multiple of 3
Case 1: 2 are multiple of 3, and one any other number from (24-8) = 16 tickets
8C2 * 16C1 / 24C3 = 56/253
Case 2: all are multiples of 3.
8C3 / 24C3 = 7/253
Add both cases.
Case 1: 2 are multiple of 3, and one any other number from (24-8) = 16 tickets
8C2 * 16C1 / 24C3 = 56/253
Case 2: all are multiples of 3.
8C3 / 24C3 = 7/253
Add both cases.
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A box contains tickets numbered from 1 to 24. 3 tickets are to be chosen to give 3 prizes. What is the probability that at least 2 tickets contain a number which is multiple of 3?a)35/256b)33/220c)63/253d)43/190e)59/253Correct answer is option 'C'. Can you explain this answer?
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A box contains tickets numbered from 1 to 24. 3 tickets are to be chosen to give 3 prizes. What is the probability that at least 2 tickets contain a number which is multiple of 3?a)35/256b)33/220c)63/253d)43/190e)59/253Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A box contains tickets numbered from 1 to 24. 3 tickets are to be chosen to give 3 prizes. What is the probability that at least 2 tickets contain a number which is multiple of 3?a)35/256b)33/220c)63/253d)43/190e)59/253Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A box contains tickets numbered from 1 to 24. 3 tickets are to be chosen to give 3 prizes. What is the probability that at least 2 tickets contain a number which is multiple of 3?a)35/256b)33/220c)63/253d)43/190e)59/253Correct answer is option 'C'. Can you explain this answer?.
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