Question

Outside a​ home, there is a 7​-key keypad numbered 1 through 7. The correct five​-digit code will open the garage door. The numbers can be repeated in the code. ​(a) How many codes are​ possible? ​(b) What is the probability of entering the correct code on the first​ try, assuming that the owner​ doesn't remember the​ code?

Answer 1

Answer:

a: 16807

b: 0.0000595

Step-by-step explanation:

(a): We have 7 possibilities of numbers, and we need to choose 5 numbers that can repeat. So, for each of the 5 numbers, we have 7 possibilities. To determine how many codes are possible, we just need to multiply the number of possibilities of each of the 5 numbers, so we have 7x7x7x7x7, or 7^5, which is 16807 possibilities.

(b): to put the correct code in the first try, we need to find the exact combination (just one combination) among these 16807 possibilities, so the probability is 1/16807, which is 0.0000595, or 0.00595%.

Answer 2

Answer:

a) 16807

b) 0.0000595

Step-by-step explanation:

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