The eight-grade class at a grade school has 13 girls and 11 boys. How many differnt boy-girl dates can be arranged?

Question

anonymous · Answer

i guess 78 but not sure

kropot72 · Answer

The number of combinations of the 24 students taken 2 at a time is 24C2, however 13C2 of these are girl-girl combinations and 11C2 are boy-boy combinations. therefore the number of different boy-girl dates that can be arranged is given by:
24C2 - 13C2 - 11C2.

zarkon · Answer

$$_{24}C_2 ~- ~_{13}C_2 ~- ~_{11}C_2=13\times 11$$

kropot72 · Answer

@Zarkon has the simplest method of solution. Each of the 11 boys can be paired with any one of the 13 girls, giving a total number of different boy-girl dates of 13 * 11.