5 digits numbers is formed by using the digits 0,1,2,3,4 and 5 without repetition. find the probability that the number is divisible by 6?

pls help out here, confuse!

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- Jan 13th 2012, 04:56 AMlawochekelbinomial problem!
5 digits numbers is formed by using the digits 0,1,2,3,4 and 5 without repetition. find the probability that the number is divisible by 6?

pls help out here, confuse! - Jan 13th 2012, 06:23 AMSorobanRe: binomial problem!
Hello, lawochekel!

I'll explain it using baby-steps.

Quote:

Five-digit numbers are formed by using the digits {0,1,2,3,4,5} without repetition.

Find the probability that the number is divisible by 6.

There are possible five-digit numbers.

To be divisible by 6, the number must be:

. . (1) divisible by 3 ... the sum of its digits must be divisible by 3.

. . (2) even ... the last digit must be even.

There are two sets of digits whose sums are divisible by 3:

. .

Consider

The last digit must be even: , 3 choices.

The other four digits can be arranged in ways.

Hence, there are:. numbers divisible by 6.

Consider

The last digit must be even: , 2 choices.

The other four digits can be arranged in ways.

Hence, there are:. more numbers divisible by 6.

Hence, there are:. numbers which are divisible by 6.

Therefore:.

- Jan 13th 2012, 08:07 AMPlatoRe: binomial problem!