Word and envelope based problems
Word based problems
Ex:

If the letters of the word FLOWER are arranged at random, then the probability that the order of the consonants is not changed is

Sol:

Total number of letters in the word FLOWER is (T) = 6

In which 2 vowels and 4 consonants

∴ n(s) = 6 !

Let E be the event of getting the order of the consonants is not changed

∴ n(E) =

∴ Required probability =
=

Short cut method:

The probability that the order of the consonants is not changed = =

Envelope based problems
Ex:

Three letters are to be sent to different persons and addresses on the envelopes are also written. without looking at the addresses, the probability that the letters go into the right envelope is

Sol:

Total number of letters in the word FLOWER is (T) = 6

Total number of ways placing 3 letters in three envelops = 3 !

∴ Required probability = (∵ n = 3)

=