In how many ways can an animal trainer arrange 6 lions and 5 tigers in a row so that no two lions are together?86400876518900088765

The problem can be solved using the concept of permutations and combinations.

Step 1: Arrange the 5 tigers first. They can be arranged in 5! (factorial) ways.

Step 2: Now, there are 6 spaces (before the 1st tiger, between 1st and 2nd tiger, between 2nd and 3rd tiger, between 3rd and 4th tiger, between 4th and 5th tiger, and after the 5th tiger) where the 6 lions can be placed such that no two lions are together.

Step 3: These 6 lions can be arranged in these 6 spaces in 6P6 ways (permutations of 6 lions in 6 places).

So, the total number of ways the animal trainer can arrange 6 lions and 5 tigers in a row so that no two lions are together is 5! * 6P6.

Let's calculate it:

5! = 54321 = 120 6P6 = 6! = 65432*1 = 720

So, the total number of ways = 120 * 720 = 86400.