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PostPosted: Thu, 5 Jun 2008 11:02:40 UTC 
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hi everybody
i'm having my GRE on 19 jun, so if you please i need the solutions for these problems urgently

important note: these problems may contain some typos; the website where i found these problems in, is full of typos. i tried to correct some but u may still be able to see some other typos.
thanks in advance

1) A teacher prepares a test. She gives 5 objective type question out of which 4 have to be answered . find the total ways in which they can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices.

225
816
192
100
144

2) How many 5 digit numbers are there with distinct digits?
144
27216
4386
6432
720

3) How many five digit numbers can be formed using the digits 0,2,3,4,and 5 when repetition is allowed such that the number formed
is divisible by 2 or 5 or both?
100
150
3125
1500
125

4) How many heptagons can be drawn by joining the vertices of a polygon with 10 sides ?
562
120
105
400
282

5) Four persons enter the lift of a seven storey building at the ground floor, how many ways can they get out of the lift on any floor other than the ground floor
720
1296
1663
360
2500

6) Ten different letters of an alphabet are given , 2 of these letters followed by 2 digits are used to number the products of a company. In how many ways can the products be numbered ?

52040
8100
5040
1000
4000

7) A box contains 5 red and 4 blue balls . in how many ways can 4 balls be chosen such that there are at most 3 balls of each colour

132
242
60
120
240

if you please, send me the explanations for these problems
thanks
i've mistakenly posted these problems into Foundation Forum

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Last edited by samarfadl on Thu, 5 Jun 2008 15:04:08 UTC, edited 1 time in total.

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PostPosted: Thu, 5 Jun 2008 12:19:19 UTC 
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2) How many 5 digit numbers are there with distinct digits?

There are nine possibilities (1 through 9) for the first digit, nine for the second, eight for the third, seven for the fourth, and six for the fifth. Hence the total number of possibilities is 9 × 9 × 8 × 7 × 6, i.e., 27216.

3) How many five digit numbers can be formed using the digits 0,2,3,4,and 5 when repetition is allowed such that the number formed is divisible by 2 or 5 or both?

There are four possibilities for the first digit (2 through 5), five for the second, five for the third, five for the fourth, and four for the fifth (0, 2, 4 and 5). Hence the total number of possibilities is 4 × 5 × 5 × 5 × 4, i.e., 2000.

6) Ten different letters of an alphabet are given; 2 of these letters followed by 2 digits are used to number the products of a company. In how many ways can the products be numbered?

There are ten possibilities for the first letter and nine for the second (since two of the ten letters are used, not one letter written twice). I think the wording would allow the digits to be the same, however, so there are one hundred possibilities for the digits (00 through 99). Hence there are a total of 9000 possible product numbers.

7) A box contains 5 red and 4 blue balls; in how many ways can 4 balls be chosen such that there are at most 3 balls of each colour?

Three ways - one red and three blues, two reds and two blues, and three reds and one blue.


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PostPosted: Thu, 5 Jun 2008 13:44:19 UTC 
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1) You may skip the first question which gives you 3 choices for the second question and 4^3 choises for the thre last questions. If you skip the second question the numbers are the same giving you 2 * 3 * 4^3 alternatives while skipping one oft the two first questions. By the same reasoning skipping one of the tre last questions gives you 3 * 3^2 * 4^2 different ways of answering. All in all you'll have 816 ways of answering the test. I have assumed that answering all five questions is not an option.

4) This is equivalent to drawing 7 items from ten. It can be done in 10 * 9 * 8 / 2 * 3 which gives 120.

5) There are 6 *5 / 2 ways of exiting the lift without regard to who is leaving the lift. The four persons can be orderes in 4! ways. Which means there are 360 ways of doing this.


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PostPosted: Thu, 5 Jun 2008 14:14:35 UTC 
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Hello, samarfadl!


Quote:
4) How many heptagons can be drawn by joining the vertices
of a polygon with 10 sides ?
. . 562  \qquad 120  \qquad 105 \qquad 400  \qquad 282

Choose 7 of the 10 vertices.

There are: .{10\choose7} \:=\:\frac{10!}{3!7!} \:=\:\boxed{120} ways.



Quote:
5) Four persons enter the lift of a 7-story building at the ground floor.
How many way ways can they get out of the lift on any floor other than the ground floor ?
. . 720 \qquad 1296  \qquad 1663 \qquad 360 \qquad 2500

Each of the four people has a choice of 6 floors.

There are: .6^4 \:=\:\boxed{1296} ways.



Quote:
7) A box contains 5 red and 4 blue balls.
In how many ways can 4 balls be chosen such that there are at most 3 balls of each colour?
. . 132 \qquad 242 \qquad 60 \qquad 120 \qquad 240

Note that we do not want four balls of the same color.


There are: .{9\choose4} \:=\:126 possible draws.

There are: .{5\choose4} \:=\:5 ways to get 4 red balls.
There are: .{4\choose4} \:=\:1 way to get 4 blue balls.
. . Hence, there are: .5 + 1 \:=\:6 ways to get all reds or all blues.

Therefore, there are: .126 - 6 \:=\:\boxed{120} ways to get at most 3 of one color.



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PostPosted: Thu, 5 Jun 2008 14:20:12 UTC 
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5) Of course! I assumed that only one person got off at a specific floor. Shame on me.


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PostPosted: Thu, 5 Jun 2008 15:01:50 UTC 
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hiii everybody :)
thank you so much guys for your reply
i would like to thank all of you
thank u skipjack
thank u to.by
thank u Soroban
:) :) :)

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PostPosted: Sat, 12 Jun 2010 19:56:36 UTC 
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[quote="skipjack"].) a no. when divided by 180 gives a remainder 98.what will be the remainder when the same no. is divided by 15 ?

a.2 b.4 c.6 d.8 e.10

2.) if the no. 23*56 is divisible by 11,then, what is the value of * ?

a.0 b.1 c.3 d.2 e.4

3.) during an experiment, temperature was measured three times. the second reading was 10 degrees lower than first, and the third was 15 degrees lower than the second. if the first reading was 5 degrees, what was the last ?

a.10/3 b.-50/3 c.27/3 d.-46/5 e.none

4.) the sum of first two of three consecutive odd numbers is 33 more than the third number. what is the second no. ?

a.35 b.39 c.37 d.33 e.none

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PostPosted: Sat, 12 Jun 2010 19:57:07 UTC 
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skipjack wrote:
.) a no. when divided by 180 gives a remainder 98.what will be the remainder when the same no. is divided by 15 ?

a.2 b.4 c.6 d.8 e.10

2.) if the no. 23*56 is divisible by 11,then, what is the value of * ?

a.0 b.1 c.3 d.2 e.4

3.) during an experiment, temperature was measured three times. the second reading was 10 degrees lower than first, and the third was 15 degrees lower than the second. if the first reading was 5 degrees, what was the last ?

a.10/3 b.-50/3 c.27/3 d.-46/5 e.none

4.) the sum of first two of three consecutive odd numbers is 33 more than the third number. what is the second no. ?

a.35 b.39 c.37 d.33 e.none

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