Combinations, Permutations and Truth Tables

1. (a) How many license plates can a state produce if the plates can contain 6 characters (from 26
letters and 10 digits) if they can only use one digit?

(b) How many ways can Mr. Paul choose 6 students from a class of 15 Boys and 12 Girls, if he
must choose at least 5 boys?

(c) How many orderings are there of the letters of the word STRAWBERRYALARMCLOCK ?

(d) How many ways can I seat 12 people around a circular table, if a certain pair of people cannot
sit next to one another?

(e) How many ways can I fill a box of 50 chocolates from 10 types if I must have at least 1 of each
type in the box?
3. (a) For a collection of 80 coins, if 53 are quarters, 15 are quarters from the 1990's, and 24 are
coins from the 1990's, what is the probability the a coin chosen at random is a quarter or is a coin
from the 1990's?
(b) What is the probability that a family with 3 children have 3 boys given they have at least 1
boy?

4. (a) Find the truth table for the Boolean Polynomial F(w,x,y,z) = wx'z + xy'
(b) Find the Disjunctive Normal Form of the polynomial in part (a).
(c) Find the Conjunctive Normal Form of the polynomial in part (a).

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