A Netherlands based gangster Rajan Madan is in India these days. He wants to rob a big bank in India, whose locker
code according to his insider info is an odd number between 50 and 450. He also knows that the numbers are from the set:{0, 1, 2, 3, 4,5). How many maximum trials he has to take to unlock the locker?
a. 110
b. 72
c. 78
d. 60
Answers
Answer:
c. 78
Step-by-step explanation:
hope it helps yOu.....
Answer:
The correct answer is option (b) 72
Step-by-step explanation:
To find,
The number of possible odd numbers between 50 and 450 using the numbers from the set {0,1,2,3,4,5}
Total number of odd numbers between 50 and 450 = Number of odd numbers between 50 and 100 + The number of odd numbers between 100 and 400 +The number of odd numbers between 400 and 450
Number of odd numbers between 50 and 100 using digits {0,1,2,3,4,5}
All the numbers between 50 and 100 are two-digit numbers
The possible digits in tens place = 5
The number of possible digits in the tens place = 1
The possible digits in the ones place = 1,3,5
The number of possible digits in the ones place = 3
Total number of possible numbers between 50 and 100 = 1×3 = 3
The number of odd numbers between 100 and 400 using digits {0,1,2,3,4,5}
The possible digits in the hundreds place = 1,2,3
The number of possible digits in the hundred's place = 3
The possible digits in the tens place = 0,1,2,3,4,5
The number of possible digits in the tens place = 6
The possible digits in the ones place = 1,3,5
The number of possible digits in the ones place = 3
Total number of possible numbers between 100 and 400 = 3×6×3 = 54
Also, 100 and 400 are not odd numbers
The number of odd numbers between 400 and 450 using digits {0,1,2,3,4,5}
The possible digits in the hundreds place = 4
The number of possible digits in the hundred's place = 1
The possible digits in the tens place = 0,1,2,3,4
The number of possible digits in the tens place = 5
The possible digits in the ones place = 1,3,5
The number of possible digits in the ones place = 3
Total number of possible numbers between 100 and 400 = 1×5×3 = 15
Hence the total possible numbers are 3+54+15 = 72
∴ The number of possible odd numbers between 50 and 450 using the numbers from the set {0,1,2,3,4,5} = 72
Hence the correct answer is option (b) 72
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