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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...
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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-

No. of waysSelecting atleast one freshmen =C13×C210+C23×C110+C33×C010 =3×10!2!×10-2!+3!2!×1!×10+1×1=166

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

No. of ways Selecting 2 freshmen and one junior=C23×C13=3!2!×1!×3!1!×2!=9

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