MAT 1460- Homework Section 9.2 Support your answer by showing your work. 1. Dete
ID: 2907164 • Letter: M
Question
MAT 1460- Homework Section 9.2 Support your answer by showing your work. 1. Determine the following: a) 6! b) P e) sCs A new restaurant offers 3-course meals with 3 choices for appetizers, 5 choices for a main course, and 4 dessert choices. How many different 3-course meals are possible? 2. The mathematics club at a university has 34 members. How many ways could they choose a president, vice-president, and treasurer? 3. A committee is to be formed consisting of 3 professors, 2 administrators, and 2 students. If they can choose from 8 professors, 7 administrators, and 6 students, how many different committes are possible? 4.Explanation / Answer
1.
a) 6! = 6*5*4*3*2*1 = 720
b) 7 P 3 = 7! / (7-3) !
= 7!/ 4!
= 210
c) 9 C 3 = 9! / (9-3)!*3!
= 9! / 6! * 3!
= 84
2.
Appetizers => 3
Main couser = >5
Desserrt =>4
Total ways = 3*5*4 = 60
3. Total members = 34
By fundamental priciple of counting
President Vice President Treasurer
34 * 33 * 32 = 35904 ways
4.
To be formed of
From 8 proffessors selecting 3 = 8 C 3
= 56
From 7 Adminstrators selecting 2 = 7 C 2
= 21
From 6 students selecting 2 = 6 C 2
= 15
Total possible committes = 56 *21*15
= 17640
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