The digits 3, 4, 5, 6 and 7 are randomly arranged to form a three-digit number. Digits are not repeated. What is the probability that the number is even and greater than 700?
To satisfy the conditions, we want the first digit to be 7. We want the last digit to either be 4 or 6. With the 7 forced to be the first digit, we have 4 digits to account for.
To get an even digit, we have a population of 2 and we are choosing 1:
We can now account for the remaining 3 digits, which is
Therefore, the number of ways to get an even number greater than 700 is:
and the probability of randomly arranging numbers into this arrangement is: