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For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?
- a)0
- b)1/16
- c)3/8
- d)7/16
- e)7/8
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
For any integer P greater than 1, P! denotes the product of all intege...
8! = 27∗32∗5∗7
Any factor of 8! can be written as 2a∗3b∗5c∗7d , where a, b, c and d are integers
a can take 8 values (0 to7)
b can take 3 values (0 to 2)
c can take 2 values (0 to 1)
d can take 2 values (0 to 1)
Any factor of 8! can be written as 2a∗3b∗5c∗7d , where a, b, c and d are integers
a can take 8 values (0 to7)
b can take 3 values (0 to 2)
c can take 2 values (0 to 1)
d can take 2 values (0 to 1)
Number of factors = 8*3*2*2
If the factor of 8! is multiple of 28, in that case-
a can take 6 values (2 to 7)
b can take 3 values (0 to 2)
c can take 2 values (0 to 1)
d can take 1 value (only 1)
a can take 6 values (2 to 7)
b can take 3 values (0 to 2)
c can take 2 values (0 to 1)
d can take 1 value (only 1)
Number of multiples of 28 = 6*3*2*1
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For any integer P greater than 1, P! denotes the product of all intege...
Understanding the problem:
Factorial of 8, denoted as 8!, is the product of all integers from 1 to 8.
We need to find the probability of choosing a multiple of 28 from the factors of 8!.
Solution:
Finding the factors of 8!
To find the factors of 8!, we need to first calculate the value of 8!.
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
Now, find all the factors of 40,320.
Factors of 40,320 are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 140, 144, 160, 168, 180, 210, 224, 240, 252, 280, 288, 315, 336, 360, 420, 480, 504, 560, 630, 672, 720, 840, 1008, 1120, 1260, 1440, 1680, 2016, 2520, 3360, 5040, 10080, 40320
Finding the multiples of 28
Multiples of 28 in the factors of 8! are: 28, 56, 84, 112, 140, 168, 196, 224, 252, 280, 308, 336, 364, 392, 420, 448, 476, 504, 532, 560, 588, 616, 644, 672, 700, 728, 756, 784, 812, 840, 868, 896, 924, 952, 980, 1008, 1036, 1064, 1092, 1120, 1148, 1176, 1204, 1232, 1260, 1288, 1316, 1344, 1372, 1400, 1428, 1456, 1484, 1512, 1540, 1568, 1596, 1624, 1652, 1680, 1708, 1736, 1764, 1792, 1820, 1848, 1876, 1904, 1932, 1960, 1988, 2016, 2044, 2072, 2100, 2128, 2156, 2184, 2212, 2240, 2268, 2296, 2324, 2352
Factorial of 8, denoted as 8!, is the product of all integers from 1 to 8.
We need to find the probability of choosing a multiple of 28 from the factors of 8!.
Solution:
Finding the factors of 8!
To find the factors of 8!, we need to first calculate the value of 8!.
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
Now, find all the factors of 40,320.
Factors of 40,320 are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 140, 144, 160, 168, 180, 210, 224, 240, 252, 280, 288, 315, 336, 360, 420, 480, 504, 560, 630, 672, 720, 840, 1008, 1120, 1260, 1440, 1680, 2016, 2520, 3360, 5040, 10080, 40320
Finding the multiples of 28
Multiples of 28 in the factors of 8! are: 28, 56, 84, 112, 140, 168, 196, 224, 252, 280, 308, 336, 364, 392, 420, 448, 476, 504, 532, 560, 588, 616, 644, 672, 700, 728, 756, 784, 812, 840, 868, 896, 924, 952, 980, 1008, 1036, 1064, 1092, 1120, 1148, 1176, 1204, 1232, 1260, 1288, 1316, 1344, 1372, 1400, 1428, 1456, 1484, 1512, 1540, 1568, 1596, 1624, 1652, 1680, 1708, 1736, 1764, 1792, 1820, 1848, 1876, 1904, 1932, 1960, 1988, 2016, 2044, 2072, 2100, 2128, 2156, 2184, 2212, 2240, 2268, 2296, 2324, 2352
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For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer?
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For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer?.
For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer?.
Solutions for For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer?, a detailed solution for For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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