Question

Find the probability that a four digit number comprising the digit 2,5,6 &7 would be divisible by 4

Answer 1

We have to find the probability of a four digit number which is formed by the digits 2,5,6 and 7 is divisible by 4.

First, Let us find how many numbers can be formed using these 4 digits without any repetition.

⇒ Total numbers = 4!

⇒ Total numbers = 24

For a four digit number to be divisible by 4, its last two digits should also be divisible by 4. Let us find it then.

___ ___ 5 2

In the blank spaces, since we have used up two numbers already. So there are about 2! ⇒ 4 numbers of this pattern.

Also,

___ ___ 7 2

As in the above situation, the two blank spaces can be filled using only two different numbers. So we have 2! = 4 numbers of this pattern.

Further,

___ ___ 5 6

Similarly here too, there are 2! = 4 numbers of this pattern.

Now there are :

⇒ 4 + 4 + 4

⇒ 12 numbers that are divisible by 4.

So,

⇒ Probability = Favourable outcomes / Possible outcomes

⇒ Probability = 12 / 24

⇒ Probability = 1 / 2

Hence, The probability of getting a four digit number which is comprised of 2,5,6 and 7 to be divisible by 4 is 1/2.

Answer 2

Given : Find the probability that a four digit number comprising the digit 2,5,6 & 7 would be divisible by 4.

Using formula :

★ Number divisible by 4 = Favourable outcomes/Possible outcomes.

Calculations :

→ Possible outcomes = 4 × 3 × 2 × 1

→ Possible outcomes = 24

→ Favourable outcomes = 2

→ Number divisible by 4 = 2/24

→ Number divisible by 4 = 1/12

Therefore, 1/2 is the divisible by 4.