In how many ways three indistinguishable Owls one Parrot and

In how many ways, three indistinguishable Owls, one Parrot and one Sparrow can sit together in a line on a string? (b) How many permutations of the letters are possible from the letters in the word: OOOPS!? (a) How many different letter arrangements can be made from the word \"DINOSAUR\"? (b) How many different letter arrangements can be made from the word \"DRAGON\"?

Solution

S.7 (a) Let us denote Owl as O, Parrot as P and Sparrow as S.

The different ways they can sit together in a line on a string are given below:

Case I: All three owls sit next to each other

O O O P S

O O O S P

P S O O O

S P O O O

P O O O S

S O O O P

Case II: Only two owls sit next to each other

O O P S O

O O S P O

O O P O S

O O S O P

O P S O O

O S P O O

P O S O O

S O P O O

O P O O S

O S O O P

P O O S O

S O O P O

Case III: None of the owls sit next to each other

O S O P O

O P O S O

Therefore, there are (6 + 12 + 2) = 20 different ways they can sit together in a line on a string. (Answer)

(b) The given word is OOOPS

The objective is to determine the number of permutations of the letters possible from the letters of the word OOOPS. The problem is similar to the earlier problem (a) as we have denoted Owl as O, Parrot as P and Sparrow as S.

Therefore the answer is 20.