木木木木

Question 1
You are organizing the annual  “Marathon Run” in which 12 individuals run through the streets of our fair city dressed as polar bears. In the following questions, determine the total number of permutations, arrangements, or combinations.
a) Suppose that there are participation prizes for everyone, but each prize differs. In how many
different ways can they be distributed to the competitors?
b) Suppose that there are four equivalent gift baskets to randomly hand out to the runners as
participation prizes. In how many different ways can they be given out?
c) Suppose that medals (gold, silver, and bronze) are to be awarded to the top three competitors
in the race. In how many ways can the prizes be awarded?
d) In a stunning development, three participants are disqualified before the race begins because of
illegal polar bear costumes. In how many ways can the four gift baskets be handed out to the
remaining competitors?

Question 2
It has been found that 20% of the applicants to XXX university were accepted in 2011. From the pile of applications from that year you randomly select three of them. What is the probability that of those three applications...
a) all were accepted?
b) one was accepted?
c) at least two were rejected?
d) the third was accepted, given that the first two were rejected?

cctv49

a) 12!
b) C12:4 = 12*11*10*9/4!
c) 12*11*10
d) C9:4 = 9*8*7*6/4!