Question

in how many ways can an animal trainer arrange 4 lion and 3 tigers in row so that no two lions are together.​

Answer 1

the answer is 12.... but not sure...:)

Answer 2

This can be done in 5! ways.

The 4 tigers should be in the 4 places marked 'T'

This can be done in 4! ways.

Therefore, the lions and the tigers can be arranged in 5! ×× 4! ways = 2880 ways.

2nd Approach :

But I want to approach in the following way :

Let all the lions appear together so that 4L = 1unit

So, there are 4 tigers + 1 Lion = 5 units

5 things can be arranged in 5!5! ways and 5 lions can be arranged themselves in 5! ways , So there are 5! ×5!×5!ways.

Total number of ways in which we can arrange 9 items = 9! ways.

Therefore condition when no two lions never appear together

= 9! - 5!×5!5!×5! = 5!( 9.8.7.6 - 5.4.3.2) = 348480

But this wrong. Please suggest thanks...