Answered: Paste Font Paragraph Styles Dictate

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Concept explainers

Topic Video

Question

Expert Solution

Step 1

Given,

There are 3 freshmen, 7 shopomores and 3 juniors.

Now for selecting atleast one freshmen, if 1 freshmen is selected then 1 freshmen is selected from 3 freshmen and the remaining 2 are selected from other 10 students. If 2 freshmen are selected then the remainng 1 is selected from other 10 students. If 3 freshmen are selected then remaining 0 is selected from the other 10 students

No of ways in which atleast one freshmen will be selected is obtained as-

$\begin{array}{rcl} N o . o f w a y s (S e l e c t i n g a t l e a s t o n e f r e s h m e n) & = & {}^{3}C_{1} \times {}^{10}C_{2} + {}^{3}C_{2} \times {}^{10}C_{1} + {}^{3}C_{3} \times {}^{10}C_{0} \\ = & 3 \times \frac{10!}{2! \times (10 - 2)!} + \frac{3!}{2! \times 1!} \times 10 + 1 \times 1 \\ = & 166 \end{array}$

Now, the no. of ways for selecting 2 freshmen and 1 junior is obtained as-

$\begin{array}{rcl} N o . o f w a y s (S e l e c t i n g 2 f r e s h m e n a n d o n e j u n i o r) & = & {}^{3}C_{2} \times {}^{3}C_{1} \\ = & \frac{3!}{2! \times 1!} \times \frac{3!}{1! \times 2!} \\ = & 9 \end{array}$

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Centre, Spread, and Shape of a Distribution$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.