Question

The Pythagorean Triple Threat is a coed softball team. League rules require the batting order to alternate boy-girl-boy-girl… (or girl-boy-girl-boy…). If there are five girls and five boys on the team, how many different batting orders are possible?

Answer 1

Answer:

28,800

Step-by-step explanation:

Orders in which boys can bat = 5! = 5×4×3×2×1 = 120

Orders in which the girls can bat = 5! =  5×4×3×2×1= 120

Each of the boys orders can pair with each of the girls orders.

Thus -

(120).(120) = 14,400

Therefore there are 14,400 pairings of boys and girls orders.

If we try to use pairing of orders to create a batting  order, either the boys can start OR the girls can start first which means there are actually 2×14,400= 28,800 possible  batting orders.

Thus 28,800 different battling orders are possible.