A four-digit number is to
be formed with the digits 0,1,2,3,4,5 without repetition. What is the
probability that this number will leave a remainder 2 when divided by 9?
Answer: 0.14
Explanation:
Required probability = (no.
of four digit numbers that leave a remainder 2 when divided by 9) / (total no.
of four digit numbers that can be formed)
If a four-digit number formed
with the digits 0,1,2,3,4,5 leaves a remainder 2 when divided by 9 then the sum
of the digits of the number should be 11. This is possible only when the digits
are (0,2,4,5) or (1,2,3,5).
With (0,2,4,5) as the
digits the number of four digit numbers that can be formed is 3 * 3! = 18
With (1,2,3,5) as the
digits the number of four digit numbers that can be formed is 4! = 24
Hence the total number of
four digit numbers satisfying the condition that can be formed is 18 + 24 =
42.
Now, the total number of
four digit numbers that can be formed with the digits 0,1,2,3,4,5 is 5*5*4*3 = 300.
Hence the required
probability = 42/300 = 0.14.