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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

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).


Solution Summary

Problems involving combinations, permutations and truth tables are solved.