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There are three bags containing natural numbers less than 10. First bag has odd numbers, second has even and the third has all the numbers. What is the probability of forming a 3 digit even number divisible by 11 if the first number is from the first bag, second from the third and the third from the second bag?
- a)41/90
- b)17/180
- c)4/45
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
There are three bags containing natural numbers less than 10. First b...
Divisibility rule of 11 says that the alternate sum of the numbers should be 0 or a multiple of 11
Let the number be abc, then a - b + c = 0 or multiple of 11, then abc is divisible by 11
First number is selected from odd numbers, second from all numbers and third from even numbers. Total possible numbers are 5 × 9 × 4 = 180
a is odd and c is even
odd - odd + even = even, so only possible way is when alternate sum is 0
odd - even + even = odd, only possible way is when alternate sum is 11
Case 1:
a = 1, b is odd, c is even -> c-b = -1 ⇒ {b,c} = {(3,2),(5,4),(7,6),(9,8)}
a = 1, b is even, c is even -> c-b = 10, no such combination of numbers
Hence, 4 cases
Case 2:
a = 3, b is odd, c is even -> c-b = -3 ⇒ {b,c} = {(5,2),(7,4),(9,6)}
a = 3, b is even, c is even -> c-b = 8, no such combination of numbers
Hence, 3 cases
Case 3:
a = 5, b is odd, c is even -> c-b = -5 ⇒ {b,c} = {(7,2),(9,4)}
a = 5, b is even, c is even -> c-b = 6 ⇒ {b,c} = {(8,2)}
Hence, 3 cases
Case 4:
a = 7, b is odd, c is even -> c-b = -7 ⇒ {b,c} = {(9,2)}
a = 7, b is even, c is even -> c-b = 4 ⇒ {b,c} = {(8,4),(6,2)}
Hence, 3 cases
Case 5:
a = 9, b is odd, c is even -> c-b = -9, no such combination of numbers
a = 9, b is even, c is even -> c-b = 2⇒ {b,c} = {(8,6),(6,4),(4,2)}
Hence, 3 cases
Total Possible cases are 16 out of 180.
Probability = 16/180 = 4/45
Hence, the correct option is (c).
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There are three bags containing natural numbers less than 10. First bag has odd numbers, second has even and the third has all the numbers. What is the probability of forming a 3 digit even number divisible by 11 if the first number is from the first bag, second from the third and the third from the second bag?a)41/90b)17/180c)4/45d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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