Combinatorics Question

[Elena89]

A British spy is trying to escape from his prison cell. The lock requires him to enter
one number, from 1-9, and then push a pair of colored buttons simultaneously. He
can make one attempt every 3 seconds. If there are 6 colored buttons, what is the
longest possible time it could take the spy to escape from the prison cell?

[shankar.ashwin]

Refer https://www.beatthegmat.com/basic-combin ... 92274.html

[neelgandham]

Longest possible time = He could open the door in the last attempt.

Total number of attempts = 9*(6!/(4!*2!))=9*15 =135
Time between attempts = 3
Number of intervals between attempts = 135-1 = 134
Total time taken =134*3 = 402 seconds

Correct me if I am wrong!

[shikh]

choosing 2 color buttons from 6 = 6C2= 15
choosing 1 number from 9= 9C1=9
==> 15*9=135
attempt every 3 secs= 135*3=405
answer is 405
am i ryt??

[fueledGMAT]

405 seconds

You first use the combination 6C2 = 15
Since there are 9 numbers to choose from, each permutation could be for the 15 possible color combinations, so 15x9 = 135

Since the spy can only use one of the 135 possible combinations every 3 seconds, the maximum amount of time is 135x3 = 405 seconds!

Great problem (took me 1min, 42 seconds to do the math)

[fueledGMAT]

Longest possible time = He could open the door in the last attempt.

Total number of attempts = 9*(6!/(4!*2!))=9*15 =135
Time between attempts = 3
Number of intervals between attempts = 135-1 = 134
Total time taken =134*3 = 402 seconds

Correct me if I am wrong!

Bah I forgot about the time reference and intervals, you were correct to subtract 1... good show!