COUNTING Problems 1 through 5 offer practice with the multiplication rule. 1.A m
ID: 3305181 • Letter: C
Question
COUNTING
Problems 1 through 5 offer practice with the multiplication rule.
1.A man has five pairs of pants, six shirts and two pairs of shoes. How many different outfits can be formed (with apologies for any fashion faux-pas)?
2.Pennsylvania license plates use a sequence of three letters followed by four digits. How many different license plates can be formed (with apologies for any nasty words)?
3.A menu has 4 appetizers, 5 main dishes, 3. deserts, and 7 beverages. How many different meals can be formed by-selecting one choice from each category?
4.A conference offers 3 seminars at 9:00 am, 5 seminars at 10:00 am and 4 seminars at 11:00 am. You also have the option of not attending a seminar at any given hour. How many ways can you spend your morning at the conference?
5.A list of students contains 6 freshmen, 5 sophomores, 7 juniors, and 3 seniors. A committee of four students is to be formed with one student from each class. How many different committees can be formed?
Problem 6through 10 offer practice with permutations.
6.How many ways can five distinct books be arranged on a shelf?
7.How many ways can six people be arranged in a line?
8.· How many ways can the selection of a chairperson, vice-chairperson, secretary, and a treasurer be made from a committee of 11 people?
9. How many ways can 12 horses finish in the order Win, Place, and Show?
10 . How many six character strings can be formed from the 26-letter alphabet if no letter is to be repeated?
Explanation / Answer
a) Using the multiplication rule, the number of different outfits that could be formed is computed as:
= Number of different pair of pants available * Number of shirt available * Number of pair of shoes available
= 5*6*2
= 60
Therefore there are 60 different outfits possible here.
2) There are 3 letters on the plate followed by 4 digits.
Now we know that each of the three letters could be filled in 26 ways as there are a total of 26 letters that are there. Also the number of digits are 10 from 0 to 9.
Therefore total number of license plates possible would be computed as:
= 26*26*26*10*10*10*10
= 175760000
Therefore there are 175760000 different license plater possible here.
3) Number of different meals possible is computed as:
= Number of different appetizers possible * Number of main dishes * Number of desserts * Number of beverages
= 4*5*3*7
= 420
Therefore there are a total of 420 meal combinations possible here.
4) A conference offers 3 seminars at 9:00 am, 5 seminars at 10:00 am and 4 seminars at 11:00 am but there is also an option of not attending each of those seminar. Therefore the total number of ways in which we could spend the morning can be computed as:
= (3 + 1)*(5 + 1)*(4 + 1)
= 4*6*5
= 120
Therefore there are 120 ways to spend the morning.