Question

in how many ways can the letter of the word "BALLOON" be arranged so that two L's do not comes together

Answer 1

1)We'll first see what is the total number of possible permutations.
2)We'll then count the number of cases where the L's ARE together.
3)We'll subtract the second result from the first.

Assuming each letter is distinct we have 7! permutations(5040). But the order of the two L's doesn't matter. So we need to divide by 2!(2) to get 2520 permutations in total.

Now assume the double L as one object. You 'll get 6! = 720 permutations which are NOT to be counted.

2520 - 720 = 1800 such ways exist.