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Four digits 1, 2, 4 and 6 are selected at random to form a four digit number. What is the probability that the number so formed, would be divisible by 4?
- a)1/2
- b)1/5
- c)1/4
- d)1/3
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Four digits 1, 2, 4 and 6 are selected at random to form a four digit ...
Solution:
To form a four-digit number, we have to consider the following cases:
1. When the first digit is 1 or 2:
In this case, the second digit can be any of the remaining three digits, and the third digit can be any of the remaining two digits. The last digit can be either 4 or 6 to make the number divisible by 4.
Number of ways to form such a number = 2 × 3 × 2 × 2 = 24
2. When the first digit is 4:
In this case, the second digit can be any of the remaining two digits, and the third digit can be any of the remaining two digits. The last digit must be 2 to make the number divisible by 4.
Number of ways to form such a number = 1 × 2 × 2 × 1 = 4
Total number of ways to form a four-digit number using the given digits = 4 × 3 × 2 × 1 = 24
Therefore, the probability of forming a four-digit number that is divisible by 4 is:
= (Number of favourable outcomes) / (Total number of outcomes)
= (24 + 4) / 24
= 1/3
Hence, the correct answer is option D.
To form a four-digit number, we have to consider the following cases:
1. When the first digit is 1 or 2:
In this case, the second digit can be any of the remaining three digits, and the third digit can be any of the remaining two digits. The last digit can be either 4 or 6 to make the number divisible by 4.
Number of ways to form such a number = 2 × 3 × 2 × 2 = 24
2. When the first digit is 4:
In this case, the second digit can be any of the remaining two digits, and the third digit can be any of the remaining two digits. The last digit must be 2 to make the number divisible by 4.
Number of ways to form such a number = 1 × 2 × 2 × 1 = 4
Total number of ways to form a four-digit number using the given digits = 4 × 3 × 2 × 1 = 24
Therefore, the probability of forming a four-digit number that is divisible by 4 is:
= (Number of favourable outcomes) / (Total number of outcomes)
= (24 + 4) / 24
= 1/3
Hence, the correct answer is option D.
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Four digits 1, 2, 4 and 6 are selected at random to form a four digit number. What is the probability that the number so formed, would be divisible by 4?a)1/2b)1/5c)1/4d)1/3Correct answer is option 'D'. Can you explain this answer?
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