Question

a) How many different ways can be letters in each of the following words be arranged?

i)YAHOO

ii)GOOGLE

b)How many of the arrangements in (a) will have the letters ‘O ́together?

Answer 1

(a) (i) Number of ways to arrange 'Y' 'A' 'H' 'O' 'O'

Total letters in the word = 5

Since O comes two times

So total ways to arrange = $\dfrac{5!}{2!}=60$

(ii) Number of ways to arrange 'G' 'O' 'O' 'G' 'L' 'E'

Total letters in the word = 6

Since O and G comes two times

So, total ways to arrange = $\dfrac{6!}{2!\cdot 2!}=180$

(b) When two O's are together

so we have to arrange 'Y' 'A' 'H' 'OO'

Hence total ways to arrange = 4! = 24

and also we have to arrange 'G' 'OO' 'G' 'L' 'E'

Hence total ways to arrange = $\dfrac{5!}{2!}=60$