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# Q1. There are 12 empty seats in a row of a theater. In how

Author Message
Intern
Joined: 11 Jan 2005
Posts: 18
Q1. There are 12 empty seats in a row of a theater. In how  [#permalink]

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22 Jan 2005, 01:23
1
Q1. There are 12 empty seats in a row of a theater. In how many ways can 3 people be seated in the row?
OA 1320

In how many ways can they be seated next to each other in the row?
OA 60

Q2. The city council is creating an exploratory group for creating a new park. The city council consists of 20 representatives, 10 Republicans and 10 Democrats. The exploratory group will consist of 3 Republicans and 3 Democrats. How many different combinations are possible of city council members to make up the exploratory group?

A. 518,400
B. 14,400
C. 120
D. 100
E. 9

Q3. A three digit numeral with no repeated digits is made from the digits 1 through 7. wht is the probability that the number indicated is:

between 300 and 650 ?

a. 11/21
b. 22/21
c.33/21
d. 40/49
e. none

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Intern
Joined: 22 Jan 2005
Posts: 3
Location: NJ

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22 Jan 2005, 14:16
Q1. There are 12 empty seats in a row of a theater. In how many ways can 3 people be seated in the row?

No of ways = 12 P 3 = 12! / 9! = 1320

In how many ways can they be seated next to each other in the row?
ANS --> 3 ppl can be seated next to each other in 3! = 6 ways ; 3 ppl can sit as a group in 12 seats in 10 ways
Hence, total # of ways = 10 * 6 = 60

Q2. RE -- How many different combinations are possible of city council members to make up the exploratory group?

-- I get B. 14,400
Total # of combinations = 10C3 * 10C3 = 14400

Q3. A three digit numeral with no repeated digits is made from the digits 1 through 7. wht is the probability that the number indicated is:
between 300 and 650 ?

a. 11/21

-- Total # of numbers satisfying the first condition = 7 * 6 * 5 = 210
-- Total # of numbers between 300 & 650 = 210 - (Nos < 300 + Nos > 650)
Nos < 300 = 60
Nos > 650 and < 700 = 10
Nos > 700 = 30
=> Total # of nos between 300 & 650 = 210 - (60+10+30) = 110

Probability = 110 / 210 = 11/21
VP
Joined: 18 Nov 2004
Posts: 1376

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22 Jan 2005, 15:55
Ans 3:

3 digit number = 7x6x5 = 210 ways

Numbers starting with 3,4,5 = 3(1x6x5) = 90
Numbers starting with 6 = 1 x 4 X 5 = 20

Total = 110

P(e) = 110/210 = 11/21
Intern
Joined: 11 Jan 2005
Posts: 18

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23 Jan 2005, 07:58
All correct.

ps. din't check the methods/solutions though.
Director
Joined: 27 Dec 2004
Posts: 851

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23 Jan 2005, 14:16

Hello folks,

Can you please explain how you came about the number of values between 300 and 650? I know these numbers cannot be repeated but how did you calculate the number of # between a given range especially when there is a constraint? Thanks
Director
Joined: 27 Dec 2004
Posts: 851

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23 Jan 2005, 14:48
Never mind folks. I figured it out already.
Non-Human User
Joined: 09 Sep 2013
Posts: 8849
Re: Q1. There are 12 empty seats in a row of a theater. In how  [#permalink]

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12 Oct 2017, 22:28
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