Question

A combination lock is unlocked by first turning the dial clockwise to a number then counterclockwise to the second number then clockwise again to the final number. On a dial with 60 numbers ho many different combinations can be made(do not allow any repeating numbers in the combination)

Answer 1

In a combination such as this. The first number can be selected from the 60 numbers in 60C1 ways = 60

The second number can be chosen from remaining 59 [since repetition is not allowed] in 59C1 ways = 59

The third and final number can be chosen in 58C1 ways = 58

Therefore total number of different combinations in this way are = 60 x 59 x 58 = 205320

Another way to do this is selecting 3 unique numbers from 60 numbers in 60C3 ways = 34220

These 3 numbers can be arranged in 3! ways = 6

Total number of different combinations = 34220 * 6 = 205320