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!
Hello, lawochekel!
I'll explain it using baby-steps.
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:.