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If Jeff has four movies
[#permalink]
Updated on: 04 Feb 2019, 04:59

1

Bookmarks

Question Stats:

In the below question, why didnt we divide by the factorials? Isn't order not important?

If anyone can help me in solving this question please.

If Jeff has four movies, and must choose to watch either 1, 2, or 3 different movies, which of the following represents a possible number of different arrangements of movies that Jeff could watch?

Indicate all possible values.

a) 4

b) 6

c) 7

d) 9

e) 12

f) 24

If anyone can help me in solving this question please.

If Jeff has four movies, and must choose to watch either 1, 2, or 3 different movies, which of the following represents a possible number of different arrangements of movies that Jeff could watch?

Indicate all possible values.

a) 4

b) 6

c) 7

d) 9

e) 12

f) 24

Re: If Jeff has four movies
[#permalink]
10 Feb 2019, 04:39

2

Expert Reply

SKH121 wrote:

In the below question, why didnt we divide by the factorials? Isn't order not important?

If anyone can help me in solving this question please.

If Jeff has four movies, and must choose to watch either 1, 2, or 3 different movies, which of the following represents a possible number of different arrangements of movies that Jeff could watch?

Indicate all possible values.

a) 4

b) 6

c) 7

d) 9

e) 12

f) 24

If anyone can help me in solving this question please.

If Jeff has four movies, and must choose to watch either 1, 2, or 3 different movies, which of the following represents a possible number of different arrangements of movies that Jeff could watch?

Indicate all possible values.

a) 4

b) 6

c) 7

d) 9

e) 12

f) 24

The question is ARRANGEMENT, so order is important and it is a permutation question...

Three cases..

1) 1 movie - 4 arrangements one each

2) 2 movies - choose two movie in 4P2 ways, which is 4C2*2! as order matters thus \(\frac{4!}{2!2!}*2!=12\)

3) 3 movies - choose three movie in 4P3 ways, which is 4C3*3! as order matters thus \(\frac{4!}{3!1!}*3!=24\)

Thus A, E and F

_________________

Some useful Theory.

1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048

2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825

3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html

4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html

5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048

2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825

3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html

4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html

5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

If Jeff has four movies
[#permalink]
24 Jul 2021, 06:32

I like to divide problems like this into cases:

1. If Jeff watched only one movie, he had 4 choices.

2. If Jeff watched two movies, he could pick one of four movies for his first choice; then for each possible choice he made for the first movie, he could pick from 3 movies for his next choice: 4x3 = 12.

3. If Jeff watched three movies, he could pick one of four movies for his first choice, then for each possible option he could choose from 3 movies, and then for each of those choices he could choose from 2 movies that he had left over: 4x3x2 = 24.

Hence, he could have 4 possible movie arrangements, 12, or 24, depending on whether he chose to watch 1, 2, or 3 movies.

1. If Jeff watched only one movie, he had 4 choices.

2. If Jeff watched two movies, he could pick one of four movies for his first choice; then for each possible choice he made for the first movie, he could pick from 3 movies for his next choice: 4x3 = 12.

3. If Jeff watched three movies, he could pick one of four movies for his first choice, then for each possible option he could choose from 3 movies, and then for each of those choices he could choose from 2 movies that he had left over: 4x3x2 = 24.

Hence, he could have 4 possible movie arrangements, 12, or 24, depending on whether he chose to watch 1, 2, or 3 movies.

gmatclubot

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