1. In a college football training session, the defensive coordinator needs to ha
ID: 3072122 • Letter: 1
Question
1. In a college football training session, the defensive coordinator needs to have 23 players standing in a row. Among these 23 players, there are5 freshman9 sophomore juniors, and3 seniors. How many different ways can they be arranged in a row if only their class level will be distinguished? (10 points) per sir 2. How many ways are there to select 7 candidates from 12 equally qualified recent graduates for openings in an accounting firm? (Order is not important) (10 points) Orders for a computer are summarized by the optional features that are requested as follows: 3. Proportion of Orders 0.25 0.65 0.1 No Optional Features One Optional Feature More than one Optional Feature (a) What is the probability that an order requests at least one optional feature? (10 points) (b) What is the probability that an order does not request more than one optional feature? (10 points)Explanation / Answer
(1) there are 4 class level so they can be arranged among themselvs in 4! ways
5 freshmen can be arranged in 5! ways
9 sophomores can be arranged in 9! ways
6 juniors can be arranged in 6! ways
3 seniors can be arranged in 3! wahs
required number of ways=4!*5!*9!*6!*3!
(2) number of ways =12C7=792
(3a) P(at leaset one optional feature)=
=P(one optional feature)+P(more than one optional feature)=0.65+0.10=0.75
(3b)P(does not request more than one optional feature)=P(request no optional feature)+P(one optional feature)=0.25+0.65=0.9
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