SOLUTION: A combination lock has the integers 1 through 20 on its dial. Opening the lock requires a combination consisting of 3 of these integers, all different from one another and in a par
Algebra.Com
Question 1209380: A combination lock has the integers 1 through 20 on its dial. Opening the lock requires a combination consisting of 3 of these integers, all different from one another and in a particular order. How many different combinations are possible for this lock?
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
Answer: 6840
Work Shown:
20*19*18 = 6840
Explanation:
Technically it should be called a permutation lock since order matters in a permutation.
There are 20 choices for the first slot, 19 choices for the next, and 18 choices for the final slot. This countdown is happening since we cannot repeat values.
Multiply those values to get the final answer.
Another way to reach this answer is to use the nPr permutation formula with n = 20 and r = 3.
RELATED QUESTIONS
a combination lock has a total of 50 digits on the dial on its face if there are three... (answered by Alan3354)
A combination lock uses three integers in the combination, and the dial is numbered with... (answered by lmeeks54)
Hi can someone help me solve this please? I got the first answer right on figuring out... (answered by ikleyn)
The combination bike lock has four wheels, each of which has the numbers 0 through 13.... (answered by ikleyn)
A "combination" lock has a three-number "combination" where the numbers are
chosen from... (answered by jim_thompson5910)
A number lock has 8 different digits. A combination of two digits can be set to open the... (answered by Alan3354)
To open a combination lock, you turn the dial to the right and stop at a number, then you (answered by Theo)
A small combination lock on a suitcase has 5 ​wheels, each labeled with the 10 digits... (answered by ewatrrr)
7. The door on the computer center has a lock which has five buttons numbered from 1 to... (answered by ewatrrr)