Question

a combination lock requires three selections of numbers, each from 1 through 35. suppose the lock is constructed in such a way that no number may be used twice in a row, but the same number may occur both first and third. for example, 20 13 20 would be acceptable, but 20 20 13 would not. how many different combinations are possible? to answer this question, note that some combinations will consist of three different numbers, whereas in others the first and third numbers can be the same. the total number of combinations is

Answer 1

Below

Explanation:

35 choices for first number

34 choices for second number (because it cannot be same as first)

34 choices for third number ( because it cannot be same a second)

35 x 34 x 34 = 40 460 combos