Using permutations and combinations for counting.

1. V63.0233: Theory of Probability Name:
Worksheet for Sections 1.1–1.2 : Permutations and Combinations June 30, 2009
1. Among the 16 applicants for four different teaching positions in an elementary school, only
ten have master’s degrees.
(i) In how many ways can these positions be filled?
(ii) In how many ways can these positions be filled with applicants having master’s degrees?
(iii) If one of the positions requires a master’s degree, while for the others it’s optional, in how
many ways can the four positions be filled?
2. How many anagrams of the word MASSACHUSETTS can you find?
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2. 3. A student takes a true-false test of 15 questions. In how many different ways can he or she
mark this test and get
(i) three right and 12 wrong?
(ii) six right and nine wrong?
(iii) 12 right and three wrong?
4. Rework the MASSACHUSETTS problem by choosing the slots for each of the letters. For
instance, there are 13 positions for the M. Of the 12 remaining, we need to choose two for the Ts.
Of the 10 remaining, we need to choose four for the Ss, etc.
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