Question

A six-digit is to be formed from the given numbers 1, 2, 3, 4, 5 and 6. Find the probability that the number is divisible by 4.

Answer 1

If repetition is not allowed then

720 no total formed by these no from 1 to 6

In which those no which can be divided by 4 are

Last no should be even so 3 no are even

Last second no can be 1 2 3 4 5 6... Any of these

3×6 =18

Probablity is 18/720=1/40=0.025

Answer 2

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

Step-by-step explanation:

Given : A six-digit is to be formed from the given numbers 1, 2, 3, 4, 5 and 6.

To find : The probability that the number is divisible by 4 ?

Solution :

Total number of digits is 6.

Number of six digit numbers formed by these numbers is $6^6= 46656$

Divisibility of 4 is,

The last two digits is also divisible by 4.

When we make six digit numbers the end digits will be among numbers

12, 16, 24, 32, 36, 44, 52, 56, 64.

Let each two digit numbers be a one-digit number or a set indicated as X.

The possible values for X  is 9.

As digit repetition can be occurred,

The number of six digit numbers ending in each value of X would be same i.e. 6.

The total number of six digit multiples thus can be formed is

$n=6 \times6\times6\times6\times9= 11664$

The probability that the number is divisible by 4 is given by,

$P=\frac{11664}{46656}$

$P=\frac{6^4 \times 9}{6^6}$

$P=\frac{9}{36}$

$P=\frac{1}{4}$

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

#Learn more

A six digit number is to be formed from the given numbers 1,2, 3,4,5,6.Find the probability that number is divisible by 4.

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