House numbers along a street consist of two-digit numbers. Each house number is made up of nonzero digits, and no digit in a house number is repeated.

Event A is defined as choosing 6 as the first digit, and event B is defined as choosing a number less than 4 as the second digit.

A house number along this street is picked at random, with each number being equally likely and no repeated digits in a number, what is P(A and B) expressed in simplest form?

Question

House numbers along a street consist of two-digit numbers. Each house number is made up of nonzero digits, and no digit in a house number is repeated.
 
Event A is defined as choosing 6 as the first digit, and event B is defined as choosing a number less than 4 as the second digit.
 
A house number along this street is picked at random, with each number being equally likely and no repeated digits in a number, what is P(A and B) expressed in simplest form?

anonymous · Answer

number of possible house number is 
$$9\times 8=72$$

anonymous · Answer

9 nonzero digits for the first number and then 8 for the second since no numbers are repeated.

anonymous · Answer

you want house number 64 and there is only one of those, so answer should be 
$$\frac{1}{72}$$