JCCDQBHWHCB014 Combinatorics : Permutations & Multiplication Principle

Suggested Approach and Solution:-

     Since the order is important, we use permutations (which are just multiplications) instead of combinations.  No over-counting or division is involved.

 

The guys can be chosen and arranged in ¹⁰P₃ = 10 x 9 x 8 = 720 ways.

The gals can be chosen and arranged in ⁶P₃ = 6 x 5 x 4 = 120 ways.

Total number of ways = 720 x 120 = 86 400 ways.