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suppose a certain combination lock requires three selections of numbers, each from 1 through 25. (a) how many different combinations are possible? (b) suppose the locks are constructed in such a way that no number may be used twice. how many different combinations are possible?

Answer :

The number of combination possible = 15625

When the numbers are repeating

The number of possible combinations = 13800

Given that a certain combination lock requires three selections of numbers

Total possible numbers = 25

Part a

Total number of combinations possible = 25 × 25 × 25

Multiply the numbers

= 15625 possible combinations

Part b

The given condition is no number may be used twice

Total number of combinations possible = 25 × 24 × 23

Multiply the numbers

= 13800 possible combinations

Therefore, when the number are repeating, the possible combinations are 15625 and when the numbers are not repeating the possible combinations are 13800

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