A company produces combination locks, the combination consist of three numbers from 0 to 39 inclusive . Because of the construction no number can occur twice in a combination. How many different combinations for locks can be attained?
Couldn’t understand the meaning of the line “the combination consist of three numbers from 0 to 39”? Please clarify.
three numbers are taken from 0 to 39. example of one such combination is 0, 27,39
since no repetition is allowed no. of combinations=40c3
these no.s can also be arranged in 3! ways to get different combinations
therefore total combinations=40c3*3!
First number can be chosen in 40 ways
Second can be chosen in 39 ways (as no repetition is allowed)
Third can be chosen in 38 ways
Answer= 40 x 39 x 38