Question

. In how many ways can the letters of the word BALLOON be arranged so that two L’s donot come together

Answer 1

total 900 ways

hope it will help

Answer 2

The number of ways in which the letters of the word BALLOON can be arranged so that two Ls do not come together is 900.

In the normal case( without any conditions):

Total no. of arrangements = 7!/[2!*2!]

[ 2!*2! is for the repetition of two letters 'L' and 'O']

In case of the given condition[ with the two Ls together]

No. of arrangements with the Ls together=  6!/2!

[ Note: The two Ls are fixed and considered as one entity. The rest of the letters can rearrange along the with fixed entity]

Therefore, no. of possible arrangements without the two Ls together =

7!/ (2!*2!) - 6!/2!

= 1260 -360 =900.