Question

At the Guelph University presentation they gave out prizes! 15 people were at the presentation. The first 2 names drawn got t-shirts, the next 3 different names drawn were given hats and the last 5 different students were given key chains. How many different ways can the prizes be handed out?

Show your calculations.

Answer 1

Solution:
Given in the question
Total number of people = 15
If First two names drawn got t-shirts than number of ways first name drawn for t-shirts out of 15 = 15C2
Now number of people left = 15-2 = 13
Next three different names drawn were given hats than number of ways next 3 different names drawn out of 13 = 13C3
Number of people left = 10
Last 5 different students were given key chains so number of ways last 5 different students out of 10 = 10C5
So Total number of different ways can the prizes be handed out = 15C2*13C3*10C5 = 105*286*252 = 7567560