# Combinations, Permutations and Truth Tables

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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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Problems involving combinations, permutations and truth tables are solved. How many orderings are there of the letters of the word STRAWBERRYALARMCLOCK is found.

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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?

One position will have a choice of 10 digits, and the other 5 can only be filled with just the 26 letters. Since the digit can be any of the 6 positions, the total number is 6*10*265 = ???

(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?

Mr. Paul can choose 5 boys in C(15,5) ways. He can choose the sixth student by C(22,1). The total number of ways is C(15,5)*C(22,1) = ???

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

The 20 letters breakdown 1 S, 1 T, 4 R, 3 A, 1 W, 1 B, 1 E, 1 Y, 2 L, 1 M, 2 C, 1 O, 1 K: If ...

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