my approach...
we need to select 2 keys out of 4 to be chosen correctly. we can get this in 4C2 ways, or 6 ways.
now..we have 4 doors...
to unlock the first one - 1/4
to unlock the second one - 1/3
we are left with 2 keys..we need to make sure that they do not match
probability that one key doesn't match 1/2
probability that the other one doesn't match 1.
now..probability that 2 are unlocked and 2 not:
1/4 * 1/3 * 1/2 * 1 = 1/24
since there are 6 possible arrangements, multiply 1/24 with 6.
1/4
C
...
we need to select 2 keys out of 4 to be chosen correctly. we can get this in 4C2 ways, or 6 ways.
now..we have 4 doors...
to unlock the first one - 1/4
to unlock the second one - 1/3
we are left with 2 keys..we need to make sure that they do not match
probability that one key doesn't match 1/2
probability that the other one doesn't match 1.
now..probability that 2 are unlocked and 2 not:
1/4 * 1/3 * 1/2 * 1 = 1/24
since there are 6 possible arrangements, multiply 1/24 with 6.
1/4
C
...
