The combinations on the lockers at the highschool consist of three numbers, each ranging from 0 to 39. If a combonation is chosen at random, what is the probablity that the first two numbers are multiples of 9, and the third number is a multiple of 4?
To find the probability, we need to first determine the total number of possible combinations, and then find the number of combinations that satisfy the given conditions.
There are 40 possible choices for each number on the locker (0 to 39). Hence, the total number of possible combinations is 40 * 40 * 40 = 64,000.
Now let's calculate the number of combinations that meet the given conditions.
For the first two numbers to be multiples of 9, we need to identify how many multiples of 9 exist in the range of 0 to 39.
The multiples of 9 between 0 and 39 are 9, 18, 27, and 36. Thus, we have 4 possible choices for each of the first two numbers, giving us a total of 4 * 4 = 16 combinations so far.
For the third number to be a multiple of 4, we need to identify the multiples of 4 between 0 and 39.
The multiples of 4 between 0 and 39 are 0, 4, 8, 12, ..., 36. There are 10 multiples of 4 in this range. Consequently, we have 10 choices for the third number.
Therefore, the total number of combinations that meet the given conditions is 16 * 10 = 160.
Finally, we can calculate the probability by dividing the number of favorable outcomes (160) by the total number of possible outcomes (64,000).
Probability = Number of favorable outcomes / Total number of possible outcomes
= 160 / 64,000
= 1 / 400
So, the probability that the first two numbers are multiples of 9, and the third number is a multiple of 4, is 1/400.