Question

A four-digit number is formed by using digits 2, 4, 6 and 8 without repetition. What is the probability that the number is divisible by 4?

Answer 1

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Answer 2

The probability that the 4-digit number is divisible by 4 is $\frac{1}{2}$.

Given:

A four-digit number is formed by using digits 2, 4, 6 and 8 without repetition.

To Find:

The probability that the number is divisible by 4

Solution:

We can simply solve this problem by using the following mathematical process.

Since the number of digits is 4 and the number is formed without repetition, the total number of 4-digit numbers that can be formed is 4!

4×3×2×1

24

Now,

According to the divisibility rule of 4, the last two digits of the number thus formed should be a multiple of 4

So, the last 2 digits can be 24,28,48,64,68 and 84 and there will be 2 possibilities for each

Therefore, the number of possible outcomes = 6×2

12

Probability = Number of possible outcomes ÷ Total number of outcomes

Probability = 12÷24

Probability = $\frac{1}{2}$

Hence, The probability that the 4-digit number is divisible by 4 is $\frac{1}{2}$

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