Permutation Question

Question

How many permutations are there of the letters in the word BASKETBALL, if the two Ls must be together?

Answer 1

There are 10 letters in the word BASKETBALL. However, we will look at the number of unique arrangements of "BASKETBAL" with just 1 "L". Then we can add another "L" in each unique arrangement of "BASKETBAL" to get a unique arrangement of "BASKETBALL" with 2 L's together.

"BASKETBAL" has 9 letters.

9! = 9 × 8 × 7 ... × 2 × 1 = 362,880 ways to arrange those letters.

B's and A's are repeated in the arrangement.

9! / (2!)*(2!) = 362,880/4 = 90,720 permutations

Answer 2

Vinu

There are 9 ways we can place the 2 L's together : 1st/2nd place, 2nd/3rd etc

Once the L's are placed there are 8 other places to fill

These can be filled in 8! ways (if no letters were repeated)

Because we have double B and A we need to divide the 8! by 2 (as we can interchange the 2 Bs) and do the same because of the As.

So number of ways of placing those 8 is 8 ! / 2 ! 2 !

So total ways = 9 x 8 ! / 2! 2! = 90720

Mike