The number of ways in which the letters of the word BALLOON can be arranged so that two L’s do not come together, is

Given word is BALOON.

Condition is the 2 L’s do not come together.

The letters B, A, O, O, N can be arranged in $\frac{5!}{2!}$ ways.

There are 6 places between them

                   -B-A-O-O-N-to arrange both L's

The no of permutations $=\frac{5!}{2}\times \frac{6{\mathrm{P}}_2}{2}=60\times 15=900$