Solution of QUIZ 1. M262 Section 2. (09.02.2022).

Solution of QUIZ 1. M262 Section 2. (09.02.2022).


1. 7 red and 7 blue pencils are randomly distributed to 7 girl and 7 boy students
such that each student gets one pencil. Find the probability that each girl student
gets a red pencil.

Solution: |S| = 14!. We should distribute red pencils to girl and blue pencils to boy
students. Therefore,


7! · 7! 1
P = = .
14! 3432

2. 12 balls are randomly distributed to 5 boxes. Find the probability that exactly
three boxes will be empty.

Solution:
 
|S| = 512 . We choose the empty boxes in 53 ways. The 12 balls go to the remaining
boxes in 212 ways, from this we subtract cases when all balls go to the same box:
212 − 2. Answer:
 
5
3
· (212 − 2)
P = .
512




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