Answer to Question #214463 in Statistics and Probability for cola

Question

what the 3 digit number in how many three-digit numbers can be formed from the set 0,1,2....9 if repetitions are allowed and the number must be divisible by 25?

Answer 1

Two conditions are given, repetitions are allowed and the number must be divisible by 25.

Note: Zero is divisible by any integer.

There are 10 integers, 0,1,2,3,...,9.

Therefore, there are 9 ways of choosing the first digit.

For a number to be divisible by 25, the last 2 digits should be zeros or divisible by 25.

Thus, the possible values of the last two digits are 00,25,50 or 75. There are 4 ways of selecting the last 2 digits.

The number of three-digits numbers that can be formed is $9\times 4=36$

Answer: 36